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Vector graphics (3,095 words) [view diff] case mismatch in snippet view article find links to article

Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as

Scalable Vector Graphics (SVG) is an XML-based vector image format for defining two-dimensional graphics, having support for interactivity and animation

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces

In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms

(usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued

polar vector × polar vector = axial vector axial vector × axial vector = axial vector polar vector × axial vector = polar vector axial vector × polar

represented by capital letters in bold, e.g. A; vectors in lowercase bold, e.g. a; and entries of vectors and matrices are italic (they are numbers from

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude

Inkscape is a vector graphics editor. It is used for both artistic and technical illustrations such as cartoons, clip art, logos, typography, diagrams

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance

linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation

Adobe Illustrator is a vector graphics editor and design software developed and marketed by Adobe. Originally designed for the Apple Macintosh, development

described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics

normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination

In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite

transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle V\to W} between two vector spaces that preserves

common to all vector spaces. Linear maps are mappings between vector spaces that preserve the vector-space structure. Given two vector spaces V and W

sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There

through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been shown to be equivalent to the axiomatic

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle

In epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen such as a parasite or microbe, to another living

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional

in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is a vector quantity, describing the magnitude

and force is a vector (i.e. having both magnitude and direction), so it follows that an electric field may be described by a vector field.: 469–70  The

classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar

the vector Laplacian applies to a vector field, returning a vector quantity. When computed in orthonormal Cartesian coordinates, the returned vector field

notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and

commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in

product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V ×

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's

(from continuous tones). In contrast, line art is usually implemented as vector graphics in digital systems. Many raster manipulations map directly onto

A viral vector vaccine is a vaccine that uses a viral vector to deliver genetic material (DNA) that can be transcribed by the recipient's host cells as

several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnitude and direction). The orientation

prior to its release. Vector and the band made a brief appearance in the promotional manga Sonic the Hedgehog Story Comic. Vector then made his official

space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional

object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then

lossy compression or lossless compression. For graphic design applications, vector formats are often used. Some image file formats support transparency. Raster

numerical representations called tokens, and each token is converted into a vector via lookup from a word embedding table. At each layer, each token is then

torque vector is perpendicular to both the position and force vectors and defines the plane in which the two vectors lie. The resulting torque vector direction

the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.

In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve

cloning vectors such as plasmids and phages. In order to carry out recombination between vector and the foreign DNA, it is necessary the vector and DNA

can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which

In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle

can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle

In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve

surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane.

point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an

In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms

the lowercase Greek letter omega), also known as the angular frequency vector, is a pseudovector representation of how the angular position or orientation

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.

"matrices". In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are the more mathematically correct

dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion

inheritance local VectorMult = {} VectorMult.__index = VectorMult setmetatable(VectorMult, Vector) -- Make VectorMult a child of Vector function VectorMult:multiply(value)

independent vectors. A vector can be pictured as an arrow. The vector's magnitude is its length, and its direction is the direction the arrow points. A vector in

registers hold read-only values such as zero, one, or pi. Vector registers hold data for vector processing done by SIMD instructions (Single Instruction

normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is

Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented

A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar

spacetime represented as a four-vector (t, x, y, z). A Lorentz transformation is represented by a matrix that acts on the four-vector, changing its components

quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization

observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative

In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. An example of

theory of vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals

In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or

curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes

has a book on the topic of: X86 Assembly/AVX, AVX2, FMA3, FMA4 Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge

defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue

In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing

In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order

a vector space. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space

following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional

is the jerk. A vector-valued function y {\displaystyle \mathbf {y} } of a real variable sends real numbers to vectors in some vector space R n {\displaystyle

Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type

model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR) Frequency domain Spectral density estimation Fourier

quantum systems using position or momentum variables and the more abstract vector quantum states. Historical, educational, and application-focused problems

with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: R v = [ cos ⁡ θ − sin ⁡ θ sin ⁡ θ cos ⁡

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic

three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying

branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner

described with respect to a reference frame. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle

respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)

with any finite or infinite number of dimensions. A Hilbert space is a vector space equipped with an inner product operation, which allows lengths and

analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism) such that P ∘ P = P {\displaystyle P\circ

theorem in vector calculus on R 3 {\displaystyle \mathbb {R} ^{3}} . Given a vector field, the theorem relates the integral of the curl of the vector field

architectures are then considered "short-vector" architectures, as earlier SIMD and vector supercomputers had vector lengths from 64 to 64,000. A modern supercomputer

The NeXT character set (often aliased as NeXTSTEP encoding vector, WE8NEXTSTEP or next-multinational) was used by the NeXTSTEP and OPENSTEP operating systems

slightly. A random vector (that is, a random variable with values in Rn) is said to be a white noise vector or white random vector if its components each

description of a fixed-layout flat document, including the text, fonts, vector graphics, raster images and other information needed to display it. PDF

Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to

linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle

Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to

mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed

approximately 9,000. The Vector won the Honor Rating of First Class from the Associated Collegiate Press in 1989–1990. The Vector is a current member of

tangent vector at all. Since a vector field on N determines, by definition, a unique tangent vector at every point of N, the pushforward of a vector field

or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol

Spark Arena (also known as Auckland City Arena, and formerly as Vector Arena) is a multipurpose arena in Auckland, New Zealand. The venue is located at

covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing

contravariance of vectors, upper indices represent components of contravariant vectors (vectors), lower indices represent components of covariant vectors (covectors)

Comics, usually as enemies of the Hulk. The group consists of four members: Vector, the group's leader, who can repel matter telekinetically; Vapor, who can

M} is a manifold T M {\displaystyle TM} which assembles all the tangent vectors in M {\displaystyle M} . As a set, it is given by the disjoint union of

a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional

allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space. The theorem also shows that there

In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one

position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is

the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary

initialization vector (IV), for each encryption operation. The IV must be non-repeating, and for some modes must also be random. The initialization vector is used

an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The

Euclidean vectors, row or column vectors, etc., see linear algebra and vector space for details. The generators of a Lie group also form a vector space over

domain of a random vector, or essentially the number of "free" components (how many components need to be known before the vector is fully determined)

in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply

spinors (pronounced "spinner" IPA /spɪnər/) are elements of a complex vector space that can be associated with Euclidean space. A spinor transforms linearly

There are two basic types of magnetometer measurement. Vector magnetometers measure the vector components of a magnetic field. Total field magnetometers

3-dimensional vector w = (wx, wy, wz) using 4 homogeneous coordinates as w = (wx, wy, wz, 1). To translate an object by a vector v, each homogeneous vector p (written

In cryptography, an initialization vector (IV) or starting variable is an input to a cryptographic primitive being used to provide the initial state. The

Vector control is any method to limit or eradicate the mammals, birds, insects or other arthropods (here collectively called "vectors") which transmit

ImmunityBio COVID-19 vaccine, codenamed hAd5, is a non replicating viral vector COVID-19 vaccine developed by the United States-based pharmaceutical company

curvature and the arc length, are expressed via derivatives and integrals using vector calculus. One of the most important tools used to analyze a curve is the

For example: Linear algebra explains how a vector space can be given a basis, and then any vector in the vector space can be expressed in this basis. This

raster graphics and vector graphics, with further 2D and 3D variants. Many graphics programs focus exclusively on either vector or raster graphics, but

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through

scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Binary

curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that

column vectors.) The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: [ x 1 x

computer animation program developed by Adobe. Animate is used to design vector graphics and animation for television series, online animation, websites

Pr(X1 ≤ x1, ..., Xn ≤ xn) is the cumulative distribution function of the vector (X1, ..., Xn), then the joint probability density function can be computed

as the zeroth Pauli matrix σ0 ), the Pauli matrices form a basis of the vector space of 2 × 2 Hermitian matrices over the real numbers, under addition

linear transformation L : X → Y {\displaystyle L:X\to Y} between topological vector spaces (TVSs) X {\displaystyle X} and Y {\displaystyle Y} that maps bounded

is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the

example speed) and a vector (a magnitude and a direction, like velocity), a tensor field is a generalization of a scalar field and a vector field that assigns

contribution is the vector: 1 ρ 2 ∇ → ρ × ∇ → p {\displaystyle {\frac {1}{\rho ^{2}}}{\vec {\nabla }}\rho \times {\vec {\nabla }}p} This vector, sometimes called

Vector Markup Language (VML) is an obsolete XML-based file format for two-dimensional vector graphics. It was specified in Part 4 of the Office Open XML

{r_{2}-r_{1}} }{|\mathbf {r_{2}-r_{1}} |}}} is the unit vector from body 1 to body 2. It can be seen that the vector form of the equation is the same as the scalar

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under

each glyph in each face and size. This technology is largely obsolete. Vector fonts (including, and sometimes used as a synonym for, outline fonts) use

differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a

Scalable Vector Extension (SVE) is "an optional extension to the ARMv8.2-A architecture and newer" developed specifically for vectorization of high-performance

the same way. Contravariant vectors are often just called vectors and covariant vectors are called covectors or dual vectors. The terms covariant and contravariant

whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points

elements of V vectors and call elements of K scalars. If v1,...,vn are vectors and a1,...,an are scalars, then the linear combination of those vectors with those

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field:

right-hand vector is within that span. If every vector within that span has exactly one expression as a linear combination of the given left-hand vectors, then

derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change

which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function

contribution is the vector: 1 ρ 2 ∇ → ρ × ∇ → p {\displaystyle {\frac {1}{\rho ^{2}}}{\vec {\nabla }}\rho \times {\vec {\nabla }}p} This vector, sometimes called

same as the determinant of its transpose. The dot product of two column vectors a and b can be computed as the single entry of the matrix product a ⋅ b

mention that it is a vector space after an origin has been specified. This identification permits points to be viewed as vectors and vice versa. For any

Metafile (CGM) is a free and open international standard file format for 2D vector graphics, raster graphics, and text, and is defined by ISO/IEC 8632. All

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under

bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix

full length prefusion stabilized Spike protein. More specifically, the vector used is the simian group C adenovirus GRAd32, isolated from a captive gorilla

{\displaystyle i(v-{\bar {v}})} are orthogonal vectors. Also, they are both real vectors by construction. These vectors span the same subspace as v {\displaystyle

In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many

tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric field on M consists of a metric tensor at

dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1. Equivalently

In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called

tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate invariant

CorelDRAW is a vector graphics editor developed and marketed by Alludo (formerly Corel Corporation). It is also the name of the Corel graphics suite, which

{R} ^{2}} . A similar process can be used to form the direct sum of two vector spaces or two modules. Direct sums can also be formed with any finite number

in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based

algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products

AD5-nCOV, trade-named Convidecia, is a single-dose viral vector vaccine for COVID-19 that is also used as an inhaled booster. It was developed by CanSino

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket

Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket or other vehicle to manipulate the direction of the

logo, new navigation tools, and a link wizard. Vector 2022, an update to Wikipedia's previous skin Vector 2010, was announced in September 2020, and initially

rotation vector (also called Euler vector) that leads to it from the reference frame. When used to represent an orientation, the rotation vector is commonly

space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood for the zero vector. A barrelled set or a barrel

field vector, while θ1 and θ2 represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing

all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed

printer to printer, requiring program authors to create numerous drivers. Vector graphics printing was left to special-purpose devices, called plotters.

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property

In molecular cloning, a vector is any particle (e.g., plasmids, cosmids, Lambda phages) used as a vehicle to artificially carry a foreign nucleic sequence

Vector is the critical journal (sometimes called a fanzine) of the British Science Fiction Association (BSFA), established in 1958. The first issue of

defined as a vector (really pseudovector) relating the aligning torque on the object from an externally applied magnetic field to the field vector itself.

VectorLinux, abbreviated VL, was a Linux distribution for the x86 platform based on the Slackware Linux distribution, originally developed by Canadian

represents the Hadamard product, and 1 is a constant vector with elements 1. The inverse matrix-to-vector diag operator is sometimes denoted by the identically

For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication

and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively

other examples) The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are

lightlike 4-vector is orthogonal to itself. Invariance of the magnitude of a vector: The magnitude of a vector is the inner product of a 4-vector with itself

such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in

relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential

Haemosporidia, family Plasmoiidae). The disease is transmitted by a dipteran vector including mosquitoes in the case of Plasmodium parasites and biting midges

INNA-051 Vaccine description Target SARS-CoV-2 Vaccine type Viral vector Clinical data Routes of administration Intranasal

algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear

direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a

EpiVacCorona) is a peptide-based vaccine against COVID-19 developed by the Russian VECTOR Center of Virology. The lack of protective effectiveness of EpiVacCorona

rasterization (American English) is the task of taking an image described in a vector graphics format (shapes) and converting it into a raster image (a series

single-level marketing. It is the parent company of CUTCO Cutlery Corp., Vector Marketing, Ka-Bar Knives, and Schilling Forge. The company has been the

structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In

structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In

is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier

bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to

four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum

single-level marketing. It is the parent company of CUTCO Cutlery Corp., Vector Marketing, Ka-Bar Knives, and Schilling Forge. The company has been the

generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is thought of as measuring the flux through

have unit length. More technically this is referred to as an isotropic vector matrix or, in a single unit width, an octet truss. More complex variations

While a PICT preview often contains a bitmap, it could also contain a vector representation of the whole image, providing very high quality previews

linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces. The transpose or

its edges. In other words, it has the same length vectors in three-dimensional space, known as vector equilibrium. The rigid struts and the flexible vertices

representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be

vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector include

changes to a vector space basis (i.e., a coordinate rotation) but may be affected by translations (as in relative speed). A change of a vector space basis

{\displaystyle \sigma _{ij}} and relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: T ( e

traffic due to flooding. Path-vector routing is used for inter-domain routing. It is similar to distance vector routing. Path-vector routing assumes that one

{v} \times \mathbf {B} \right)} where × is the vector cross product (all boldface quantities are vectors). In terms of Cartesian components, we have: F

smaller DNA fragments. Subsequently, these fragments are then combined with vector DNA to generate recombinant DNA molecules. The recombinant DNA is then introduced

2021. Retrieved 10 July 2021. "A Phase I Clinical Trial of Influenza virus Vector COVID-19 Vaccine for intranasal Spray (DelNS1-2019-nCoV-RBD-OPT1)". chictr

the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map L : V → W between two vector spaces

{\displaystyle x} are called the tangent vectors at x {\displaystyle x} . This is a generalization of the notion of a vector, based at a given initial point,

COVID-19 vaccine Vaccine description Target SARS-CoV-2 Vaccine type Viral vector Clinical data Other names VXA-CoV2-1, VXA-CoV2-1.1-S, VXA-CoV2-3.1 Routes

is known as insect-specific bunyaviruses. A majority of bunyaviruses are vector-borne. With the exception of Hantaviruses and Arenaviruses, all viruses

and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K {\displaystyle \mathbb {K} } with an absolute value

convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex subset of a Hausdorff locally convex topological vector space is equal to

magnitude. Because each one is perpendicular to its respective position vector, simple vector subtraction implies two similar isosceles triangles with congruent

{J} =\mathbf {p} _{2}-\mathbf {p} _{1}.} Momentum is a vector quantity, so impulse is also a vector quantity: ∑ F × Δ t = Δ p . {\displaystyle \sum \mathbf

elements of the field (called scalars), and elements of the vector space (called vectors). Abstract algebra is the name that is commonly given to the

The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection

for medicine and biology. Vector analysis, also called vector calculus, is a branch of mathematical analysis dealing with vector-valued functions. Scalar

bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X

density, with units of charge per unit time per unit area. Also known as vector current, it is used in the geometric context of four-dimensional spacetime

A number of vector graphics editors exist for various platforms. Potential users of these editors will make a comparison of vector graphics editors based

mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra)

component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular

within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude

bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called

curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes

maximum in Rn by the extreme value theorem. Because the Schwartz space is a vector space, any polynomial ϕ ( x ) {\displaystyle \phi ({\boldsymbol {x}})} can

support on the extreme points of a convex set C. Roughly speaking, every vector of C should appear as a weighted average of extreme points, a concept made

every nonzero real column vector x , {\displaystyle \mathbf {x} ,} where x ⊤ {\displaystyle \mathbf {x} ^{\top }} is the row vector transpose of x . {\displaystyle

matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to

traction, also called stress vector, traction,[page needed] or traction vector. The stress vector is a frame-indifferent vector (see Euler-Cauchy's stress

gating mechanism to input or forget certain features, but lacks a context vector or output gate, resulting in fewer parameters than LSTM. GRU's performance

was intended to support execution of short "vector mode" instructions but these operated on each vector element sequentially and thus did not offer the

(SL) is a paradigm where a model is trained using input objects (e.g. a vector of predictor variables) and desired output values (also known as a supervisory

material via bulk motion. The fluid's motion is described mathematically as a vector field, and the transported material is described by a scalar field showing

Longtime supervillain Gru formulates a plan to steal the moon after his rival Vector steals the Great Pyramid of Giza. Meanwhile, he starts a family by adopting

Wikifunctions has a concat function. In formal language theory and computer programming, string concatenation is the operation of joining character strings

for new shapes by writing simple XML files, using a subset of Scalable Vector Graphics (SVG) to draw the shape. Dia loads and saves diagrams in a custom

and a unit vector for the axis, or as a Euclidean vector obtained by multiplying the angle with this unit vector, called the rotation vector (although

A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic

The shapefile format is a geospatial vector data format for geographic information system (GIS) software. It is developed and regulated by Esri as a mostly

connection on the tangent bundle), then this connection allows one to transport vectors of the manifold along curves so that they stay parallel with respect to

The KRISS Vector is a series of weapons based upon the parent submachine gun design developed by the American company KRISS USA, formerly Transformational

conjugate gradient method and GMRES utilize fast computations of matrix-vector products A x i {\displaystyle Ax_{i}} , where matrix A {\displaystyle A}

of the first dose of the Sputnik V vaccine, which is based on the Ad26 vector, and it can be stored at a normal refrigerator temperature of 2–8 °C (36–46 °F)

(1956) 45 (1964) 75 (1964) Classic (1967) 25 (1975) 180 (1977) Arrow (1982) Vector (1986) Duofold International (1987) 95 (1988) Sonnet (1993) Parker 100 (2004)

mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice

field, and a gear turning inside a mechanism. Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration

transmission can also occur via an intermediate species (referred to as a vector), which carry the disease pathogen without getting sick. The term is from

so it permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space. Connections are

may be of vector or raster type. By itself, the term "digital image" usually refers to raster images or bitmapped images (as opposed to vector images).[citation

Principle—Let X {\displaystyle X} be a Banach space, Y {\displaystyle Y} a normed vector space and B ( X , Y ) {\displaystyle B(X,Y)} the space of all continuous

information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed

analysis. Throughout the article, unless stated otherwise, the base field of a vector space is the field of real numbers or that of complex numbers. Algebras

A vector graphic editor is a computer program that enables its users to create, compose and edit images with the use of mathematical and geometrical commands

depth. Suppose V and W are vector spaces over the field K. The Cartesian product V × W can be given the structure of a vector space over K (Halmos 1974

In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization

mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include

also known as IIBR-100, is a replication-competent recombinant VSV viral vectored COVID-19 vaccine candidate. It was developed by the Israel Institute for

AdCLD-CoV19 Vaccine description Target SARS-CoV-2 Vaccine type Viral vector Clinical data Routes of administration Intramuscular Identifiers CAS Number

functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X {\displaystyle X} into

INCOVACC Vaccine description Target SARS-CoV-2 Vaccine type Viral vector Clinical data Trade names iNCOVACC Routes of administration Intranasal ATC code

Principles of Operation. The z13 introduced the Vector Facility for z/Architecture. It adds 32 vector registers, each 128 bits wide; the existing 16 floating-point

algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated

precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a

Universiti Sains Malaysia (lit. 'University of Science Malaysia'; abbreviated as USM) is a public research university in Malaysia. Founded on 1 June 1969

Given a knot vector t, a degree n, and a smoothness vector r for t, one can consider the set of all splines of degree ≤ n having knot vector t and smoothness

score to each possible category k by combining the feature vector of an instance with a vector of weights, using a dot product. The predicted category is

specific headings ("radar vectors"). The majority of IFR navigation is given by ground- and satellite-based systems, while radar vectors are usually reserved

Graphics Markup Language (PGML) is an XML-based language for representing vector graphics. It was a World Wide Web Consortium (W3C) submission by Adobe Systems

A cloning vector is a small piece of DNA that can be stably maintained in an organism, and into which a foreign DNA fragment can be inserted for cloning

genes for special circumstances. Artificial plasmids are widely used as vectors in molecular cloning, serving to drive the replication of recombinant DNA

a vector space. Specifically, when the vector space comprises matrices, such norms are referred to as matrix norms. Matrix norms differ from vector norms

mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows

with two dimensions, typically indexed by UV coordinates. 2D vector A two-dimensional vector, a common data type in rasterization algorithms, 2D computer

algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular

groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to

vector bundles, the Levi-Civita connection on the tangent bundle of a pseudo-Riemannian manifold, which gives a standard way to differentiate vector fields

special class of fiber bundles, called vector bundles, are those whose fibers are vector spaces (to qualify as a vector bundle the structure group of the bundle

algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as

be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an isotropic vector or null vector. In complex geometry, a line through

electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is scalar, the flow

physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space

In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional

functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are

an Indian vector control scientist, biologist and acarologist, known for his pioneering contributions to the control programmes against vector-borne diseases

ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence

Harmonic Vector Excitation Coding, abbreviated as HVXC is a speech coding algorithm specified in MPEG-4 Part 3 (MPEG-4 Audio) standard for very low bit

registers (GPRs) for integer operations. 64 × 128-bit vector scalar registers (VSRs) for vector operations and floating-point operations. 32 × 64-bit

finite-dimensional vector spaces, vectors and linear maps can be represented by matrices. It follows that the theories of matrices and finite-dimensional vector spaces

for straightforward derivation of magnetic field B, while the fundamental vector here is H. The Biot–Savart law: Sec 5-2-1  is used for computing the resultant

Karbon (formerly Karbon14, Kontour, and KIllustrator) is a vector graphics editor. It is a component of Calligra Suite, an integrated graphic art and office

is vector addition, where two vectors are added and result in a vector. An example of an external operation is scalar multiplication, where a vector is

single column are called column matrices. When vectors are involved, the terms row vector and column vector are commonly used instead. A matrix with the

perceptrons. In a vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it

Vector sum excited linear prediction (VSELP) is a speech coding method used in several cellular standards. The VSELP algorithm is an analysis-by-synthesis

tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in ℝ3 to

between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot

direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of

depending on the nature and interpretation of the differential equation or vector field. In physics, integral curves for an electric field or magnetic field

Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance

bundle is an operation on vector bundles extending the operation of duality for vector spaces. The dual bundle of a vector bundle π : E → X {\displaystyle

projective tensor product of two topological vector spaces (TVSs). Throughout let X,Y, and Z be topological vector spaces (TVSs) and L : X → Y be a linear

defined by its electric field vector. In the case of a circularly polarized wave, the tip of the electric field vector, at a given point in space, relates

magnetic interaction is described in terms of a vector field, where each point in space is associated with a vector that determines what force a moving charge

differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold. It may

helper dependent virus, also termed a gutless virus, is a synthetic viral vector dependent on the assistance of a helper virus in order to replicate, and

intrinsic derivative of a vector field, upon changing the coordinate system, transform as the components of a contravariant vector. This discovery was the

synthesized as part of a vector, which is designed to enter the desired host cell and deliver the transgene to that cell's genome. Vectors utilized as the method

a vector. Because of this sylvatic cycle, yellow fever cannot be eradicated except by completely eradicating the mosquitoes that serve as vectors. In

nonzero vector. The plane determined by the point P0 and the vector n consists of those points P, with position vector r, such that the vector drawn from

technical difference between vector and raster editors stem from the difference between vector and raster images. Vector graphics are created mathematically

vector lies closest to the input vector. This can be simply determined by calculating the Euclidean distance between input vector and weight vector.

cone to distinguish it from other sorts of cones—is a subset of a real vector space that is closed under positive scalar multiplication; that is, C {\displaystyle

analyzers are scalar network analyzer (SNA)—measures amplitude properties only vector network analyzer (VNA)—measures both amplitude and phase properties A VNA

equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today

{\displaystyle \mathbb {R} ^{m}} and x {\displaystyle \mathbf {x} } is a column vector with n {\displaystyle n} entries, then there exists an m × n {\displaystyle

conjugate-linear map) f : H → Y {\displaystyle f:H\to Y} is a map between vector spaces that is additive: f ( x + y ) = f ( x ) + f ( y )  for all  x , y

direction. Both force and displacement are vectors. The work done is given by the dot product of the two vectors, where the result is a scalar. When the

state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manifold. The evolution rule of the dynamical system is

over the real numbers, and certain non-Euclidean geometries. Let S be a vector space or an affine space over the real numbers, or, more generally, over

gauge covariant derivative. A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial

{r_{12}=r_{1}-r_{2}} } is the displacement vector between the charges, r ^ 12 {\textstyle {\hat {\mathbf {r} }}_{12}} a unit vector pointing from q 2 {\textstyle q_{2}}

linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} in an inner product space

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory

of matrix. A vector of ones or all-ones vector is matrix of ones having row or column form; it should not be confused with unit vectors. For an n × n

In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a

single line. This line is called the axis of rotation. Then the radius vectors from the axis to all particles undergo the same angular displacement at

The following is a list of characters from the Harry Potter series. Each character appears in at least one Harry Potter-related book or story by J. K.

(x)}N} . Hence it can be used to push tangent vectors on M {\displaystyle M} forward to tangent vectors on N {\displaystyle N} . The differential of a

which may be, for example, scalars, vectors, or tensors. Mathematical expressions involving these quantities in vector calculus and tensor analysis (such

k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which

algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors. A unit vector means that the vector has a length of

space Legendre polynomials Matrices Mercer's theorem Min-max theorem Normal vector Orthonormal basis Orthogonal complement Orthogonalization Parallelogram

vector is directed along the unit vector k {\displaystyle \mathbf {k} } which is perpendicular to the plane of movement. Introduce the unit vectors e

as mosquitoes and flies are by far the most common disease carrier, or vector. These insects may carry a parasite, bacterium or virus that is infectious

of vectors – can be generalized by allowing a broader range of scalar values and, perhaps simultaneously, by widening the definition of a vector. A motivating

analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively

k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which

COH04S1 Vaccine description Target SARS-CoV-2 Vaccine type Viral vector Clinical data Routes of administration Intramuscular Identifiers CAS Number 2716897-29-7

engine, non-destructive layers and masks, group-based layer management, vector artwork support, and switchable customisation profiles. The software is

Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance

algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors. A unit vector means that the vector has a length of

{\displaystyle (\mathbf {H} )} , maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It

{\displaystyle i} includes a scalar response y i {\displaystyle y_{i}} and a column vector x i {\displaystyle \mathbf {x} _{i}} of p {\displaystyle p} parameters (regressors)

acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket

Texas at Austin. NDV-HXP-S uses the Newcastle disease virus as its viral vector. The platform can be live or inactivated. Unlike vaccines such as Moderna's

In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the

a standard file format for representing 3-dimensional (3D) interactive vector graphics, designed particularly with the World Wide Web in mind. It has

Rayleigh distribution is often observed when the overall magnitude of a vector in the plane is related to its directional components. One example where

The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component

algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός

of constant pressure and temperature a vector potential, in electromagnetics it can refer to the magnetic vector potential with a subscript, an alternating

matrix (mij) is a logical vector or bit string. If m = 1, the vector is a row vector, and if n = 1, it is a column vector. In either case the index equaling

(stylized as cairo) is an open-source graphics library that provides a vector graphics-based, device-independent API for software developers. It provides

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar

electric field, dA is a vector representing an infinitesimal element of area of the surface, and · represents the dot product of two vectors. In a curved spacetime

described below. The dual space of a finite-dimensional vector space is again a finite-dimensional vector space of the same dimension, and these are thus isomorphic

through a Gaussian surface is zero, and the magnetic field is a solenoidal vector field. The Maxwell–Faraday version of Faraday's law of induction describes

whose transmission is impacted by climate change include, for example, vector-borne diseases like dengue fever, malaria, tick-borne diseases, leishmaniasis

Animation of Scalable Vector Graphics, an open XML-based standard vector graphics format is possible through various means: Scripting: ECMAScript is a

probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either

vector space. The case of the Real line is the easiest to explain. This type of differential is also known as a covariant vector or cotangent vector,

geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of

or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables

{x}}\cdot {\vec {n}},t),} where n → {\displaystyle {\vec {n}}} is a unit-length vector, and G ( d , t ) {\displaystyle G(d,t)} is a function that gives the field's

In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different

(some authors use VectK) has all vector spaces over a field K as objects, and K-linear maps as morphisms. Since vector spaces over K (as a field) are the

In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0);

two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate

designed by Stephan Aßmus. Aßmus also created the Haiku Vector Icon Format (HVIF), a vector storage format to store icons in Haiku, and is aimed at fast

+a_{n}^{2}}{n}}}} The Cauchy–Schwarz inequality states that for all vectors u and v of an inner product space it is true that | ⟨ u , v ⟩ | 2 ≤ ⟨ u

ARM's Scalable Vector Extension. That is, each vector in up to 32 vectors is the same length.: 25  The application specifies the total vector width it requires

screenshots are raster images, but some vector-based GUI environments like Cairo are capable of generating vector screenshots. Screenshot kits were available

exterior product of two basis vectors, and its Hodge dual is the normal vector given by their cross product; conversely, any vector is dual to the oriented

functional analysis), also called a quasi-seminorm or a Banach functional, on a vector space X {\displaystyle X} is a real-valued function with only some of the

a vector y = [y1, ..., yn]T), each associated with a fitted (or modeled, or predicted) value f1, ..., fn (known as fi, or sometimes ŷi, as a vector f)

field, the satellite had two magnetometers. The scalar (Cesium vapor) and vector magnetometers gave Magsat a capability beyond that of any previous spacecraft

concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equation System of linear equations

and Ulam. Definition: The midpoint of two elements x and y in a vector space is the vector ⁠1/2⁠(x + y). Theorem—Let A : X → Y be a surjective isometry between

half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other

\,\mathbf {A} } , of the vector field A is a vector, which is symbolically expressed by the cross product of ∇ and the vector A, curl ⁡ A = ( ∂ A z ∂ y

{\displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields { V 1 , … , V n } {\displaystyle \{V_{1},\ldots ,V_{n}\}} on the

{\displaystyle a} and b {\displaystyle b} be vectors and let F {\displaystyle F} be a multivector-valued function of a vector. The directional derivative of F {\displaystyle

K(\|x\|+\|y\|)} for some K > 1. {\displaystyle K>1.} A quasi-seminorm on a vector space X {\displaystyle X} is a real-valued map p {\displaystyle p} on X

equations. He was a pioneer in the study of moduli spaces of holomorphic vector bundles on projective varieties. His work is considered the foundation for

reservoirs and tick vectors. The survival and transmission of these tick-borne viruses are closely linked to their interactions with tick vectors and host cells

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the

reciprocal space or k space; it is the dual of physical space considered as a vector space. In other words, the reciprocal lattice is the sublattice which is

mathematical physics, gauge theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics

K(\|x\|+\|y\|)} for some K > 1. {\displaystyle K>1.} A quasi-seminorm on a vector space X {\displaystyle X} is a real-valued map p {\displaystyle p} on X

topological vector space is locally convex if and only if its topology is induced by a family of seminorms. Let X {\displaystyle X} be a vector space over

{\displaystyle a} and b {\displaystyle b} be vectors and let F {\displaystyle F} be a multivector-valued function of a vector. The directional derivative of F {\displaystyle

example, when E {\displaystyle E} is a vector bundle a section of E {\displaystyle E} is an element of the vector space E x {\displaystyle E_{x}} lying

defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude

the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the

{\displaystyle \leq 1.} In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus,

covariant vectors, but more commonly dual vectors or one-forms) are elements of the cotangent space. At p {\displaystyle p} , these two vector spaces may

a vector y = [y1, ..., yn]T), each associated with a fitted (or modeled, or predicted) value f1, ..., fn (known as fi, or sometimes ŷi, as a vector f)

adenovirus vectors, including replication incompetent types, can deliver DNA coding for specific antigens. Adenovirus have been used to produce viral vector COVID-19

lattice vectors h a 1 + k a 2 + ℓ a 3 {\displaystyle h\mathbf {a} _{1}+k\mathbf {a} _{2}+\ell \mathbf {a} _{3}} because the direct lattice vectors need not

{\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } is a function taking as input a vector x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} and outputting

Invaders and refined through trial and error. The game is rendered on a vector display in a two-dimensional view that wraps around both screen axes. Asteroids

bundle of rank one smaller than the dimension of M. Note that a symplectic vector space is always even-dimensional, while contact manifolds need to be odd-dimensional

equations. He was a pioneer in the study of moduli spaces of holomorphic vector bundles on projective varieties. His work is considered the foundation for

passing through the origin. More generally, the Grassmannian G(k, V) of a vector space V over a field F is the moduli space of all k-dimensional linear subspaces

In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the

A distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure

E_{12}={\begin{bmatrix}0&1&0\\0&0&0\\0&0&0\end{bmatrix}}} A vector unit is a standard unit vector. A single-entry matrix generalizes the matrix unit for matrices

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle

transplant or blood transfusion tend to have symptoms similar to those of vector-borne disease, but the symptoms may not manifest for anywhere from a week

distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional

Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase

( E ) {\displaystyle F(E)} of a vector bundle E {\displaystyle E} , which consists of all ordered bases of the vector space attached to each point. The

(homothecy), the linear maps from E to E that map orthogonal vectors to orthogonal vectors. The orthogonal O(n) is the subgroup of the general linear group

other causes. Further, as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For example, in optics

Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: A + B = { a + b | a ∈ A ,

that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar

mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar

a circle), a line segment is called a chord (of that curve). If V is a vector space over ⁠ R {\displaystyle \mathbb {R} } ⁠ or ⁠ C , {\displaystyle \mathbb

selects a random 3n-bit vector R and sends R to Alice. Alice selects a random n-bit vector Y and computes the 3n-bit vector G(Y). If b=1 Alice sends

the stress vector across a surface with normal direction x {\displaystyle x} is directed opposite to x {\displaystyle x} . If the stress vector itself is

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument

B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not

lateral pass, the ball is thrown backwards or sideways to a teammate with no vector of the pass trajectory towards the opponent's goal line. Glossary of American

vectors can describe finite sums (via finite-dimensional vector spaces), infinite series (via vectors in sequence spaces), and integrals (via vectors

equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried

Dobson reprising the role of Red Alert, Richard Newman as the voice of Vector Prime, Michael Dobson returning as Starscream, Ted Cole as the voice of

In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential

In differential geometry, the cotangent space is a vector space associated with a point x {\displaystyle x} on a smooth (or differentiable) manifold M

an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations

a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the ring of the coefficients is not a division

added together as vectors. In vector format, the moment can be defined as the cross product between the radius vector, r (the vector from point O to the

geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding

transformations (that is bijective mappings), the translations, which forms a vector space (over a given field, commonly the real numbers), and such that for

which is a manifold. As such, the fiber is a vector space and the tensor bundle is a special kind of vector bundle. Lee, John M. (2012). Introduction to

such a field is described by vectors at every point in space, which is, in turn, called a vector field. A conservative vector field can be simply expressed

symmetric space. In a Euclidean vector space, the reflection in the point situated at the origin is the same as vector negation. Other examples include

In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a pseudo-Riemannian manifold

and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle \mathbf {r}

repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not

image processing, motion estimation is the process of determining motion vectors that describe the transformation from one 2D image to another; usually

additive identity include: The zero vector under vector addition: the vector whose components are all 0; in a normed vector space its norm (length) is also

be vector-valued such that η ( θ ) ⋅ T ( x ) {\displaystyle \eta (\theta )\cdot T(x)} is real-valued. However, see the discussion below on vector parameters

which is a manifold. As such, the fiber is a vector space and the tensor bundle is a special kind of vector bundle. Lee, John M. (2012). Introduction to

In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus

as smooth manifolds. It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number

as a vector for elephantiasis. After this discovery, he collaborated with Ronald Ross to examine the transmission of malaria via mosquito vector. His

{B}}} on X {\displaystyle X} is called a vector bornology on X {\displaystyle X} if it is stable under vector addition, scalar multiplication, and the

the structure of a metric space, including Riemannian manifolds, normed vector spaces, and graphs. In abstract algebra, the p-adic numbers arise as elements

} where dA is an element of area vector of the moving surface Σ(t), B is the magnetic field, and B · dA is a vector dot product representing the element

_{x}\subseteq T_{x}M} of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the

as a free abelian group of dimension n {\displaystyle n} which spans the vector space R n {\displaystyle \mathbb {R} ^{n}} . For any basis of R n {\displaystyle

In mathematics, a subbundle L {\displaystyle L} of a vector bundle E {\displaystyle E} over a topological space M {\displaystyle M} is a collection of

etc. The Fréchet derivative defines the derivative for general normed vector spaces V , W {\displaystyle V,W} . Briefly, a function f : U → W {\displaystyle

an associated vector space T p M {\displaystyle T_{p}M} called the tangent space of M {\displaystyle M} at p {\displaystyle p} . Vectors in T p M {\displaystyle

contain general and technical information about publicly available raster-to-vector conversion software. Adobe Freehand (1988–2003) Adobe Streamline (1989–2001)

2014, at Vector Arena in Auckland, New Zealand. The event was the first that the organization hosted in New Zealand, it took place at the Vector Arena in

areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric)

2023 EP by Fergus McCreadie Sketch (software), a vector graphics editor Skencil, formerly Sketch, a vector graphics editor Sketch, an approximation of some

The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented

torsion tensor is a bilinear map of two input vectors X , Y {\displaystyle X,Y} , that produces an output vector T ( X , Y ) {\displaystyle T(X,Y)} representing

were released to supplement Perfect Dark Zero. The first novel, Initial Vector, was written by Greg Rucka and released in 2005. It is set six months after

Philippine-registered passenger ferry that sank after it collided with the oil tanker Vector on December 20, 1987. Built by Onomichi Zosen of Hiroshima, Japan, the ship

some other geometries, the triangle inequality is a theorem about vectors and vector lengths (norms): ‖ u + v ‖ ≤ ‖ u ‖ + ‖ v ‖ , {\displaystyle \|\mathbf

for example Higgs-like fields. Vector fields, which associate a vector to every point in space. Some examples of vector fields include the electromagnetic

many vector subchannels of vector size M {\displaystyle M} . There is no ISI across these vector subchannels but there is ISI inside each vector subchannel

force vector m {\displaystyle m} is the mass of the body on which the force is acting a {\displaystyle \mathbf {a} } is the acceleration vector, the second

longitude is taken to be the positive x-axis. k is the unit vector (0, 0, 1), which is the normal vector to the xy reference plane. For non-inclined orbits (with

then the nonzero tangent vectors at each point in the manifold can be classified into three disjoint types. A tangent vector X {\displaystyle X} is: timelike

In functional analysis, an F-space is a vector space X {\displaystyle X} over the real or complex numbers together with a metric d : X × X → R {\displaystyle

usually as vectors, matrices, or tuples. The similarity of the query vector and document vector is represented as a scalar value. Vector space model

theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and

vector. Within the life-cycle stages taking place in the vector, density-dependence may influence the development of L3 larvae in vectors and vector life

an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. Applying this to the

per second is the unit of both speed (a scalar quantity) and velocity (a vector quantity, which has direction and magnitude) in the International System

transformations, for example, a future-pointing timelike vector would be inverted to a past-pointing vector Some elements have orientation reversed by improper

bounded. Under the definition below, the same holds for any topological vector space (not necessarily Hausdorff nor complete). The general logical form

elementary abelian p-group is a vector space over the prime field with p elements, and conversely every such vector space is an elementary abelian group

The Goodyear Tire & Rubber Company is an American multinational tire manufacturer headquartered in Akron, Ohio. Goodyear manufactures tires for passenger

manifold, and X ( M ) {\displaystyle {\mathfrak {X}}(M)} be the space of all vector fields on M {\displaystyle M} . We define the Riemann curvature tensor as

of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension

diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional

in transverse polarization (perpendicular to the direction of the wave vector). A mathematical description of wave propagation in a birefringent medium

In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle

AVX-512 are 512-bit extensions to the 256-bit Advanced Vector Extensions SIMD instructions for x86 instruction set architecture (ISA) proposed by Intel

group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian

two-coordinate description of the plane was later generalized into the concept of vector spaces. Many other coordinate systems have been developed since Descartes

two vectors. One is the cross product of the velocity and magnetic field vectors. Based on the properties of the cross product, this produces a vector that

in transverse polarization (perpendicular to the direction of the wave vector). A mathematical description of wave propagation in a birefringent medium

body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided

{\mathbf {r-r_{i}} }{|\mathbf {r-r_{i}} |}}} is the unit vector of the displacement vector that indicates the direction of the field due to the source

from Donald Knuth's Metafont language and interpreter. MetaPost produces vector graphic diagrams from a geometric/algebraic description. The language shares

Extensible Application Markup Language (XAML /ˈzæməl/ ) is a declarative XML-based language developed by Microsoft for initializing structured values and

group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian

a vector space is the maximum size of a linearly independent subset. In a vector space consisting of a single point (which must be the zero vector 0)

assigned to each word in a sentence. More generally, attention encodes vectors called token embeddings across a fixed-width sequence that can range from

stable vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle

numerical value and kg is the unit symbol (for kilogram). Quantities that are vectors have, besides numerical value and unit, direction or orientation in space

in a vector space is a set S {\displaystyle S} which can be "inflated" or "scaled up" to eventually always include any given point of the vector space

partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions

: in std_logic_vector(2 downto 0); a2 : in std_logic_vector(2 downto 0); a3 : in std_logic_vector(2 downto 0); a4 : in std_logic_vector(2 downto 0); sel

system. The Cray-1 was the first supercomputer to successfully implement the vector processor design. These systems improve the performance of math operations

neighborhood Vector bundle – a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps. Vector field – a section of a vector bundle

hyperplane can be defined by its normal vector, a unit vector v → ∈ V {\textstyle {\vec {v}}\in V} (a vector with length 1 {\textstyle 1} ) that is orthogonal

by researchers at Google. It learns to represent text as a sequence of vectors using self-supervised learning. It uses the encoder-only transformer architecture

a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through

trix}}={\begin{bmatrix}0&1\\0&1\end{bmatrix}}} The vector product (or cross product) of two vectors in three dimensions is anti-commutative; i.e., b ×

topological vector space (TVS) in which an analog of Montel's theorem holds. Specifically, a Montel space is a barrelled topological vector space in which

{PQ}}} denotes the vector defined by the two points P and Q, which can be identified with the translation that maps P to Q. The same vector can be denoted

only on elephant shrews. The oriental rat flea, Xenopsylla cheopis, is a vector of Yersinia pestis, the bacterium that causes bubonic plague. The disease

generalization of the notion of a coordinate frame (an ordered basis of a vector space, in conjunction with an origin) often used to study the extrinsic

occasionally called cofunctors. There is a convention which refers to "vectors"—i.e., vector fields, elements of the space of sections Γ ( T M ) {\displaystyle

of "capabilities" Cached information on access-decisions via the Access Vector Cache (AVC) Default-deny policy (anything not explicitly specified in the

distribution of a quadratic function of a multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal

triangle inequality. Even more common, M is taken to be the d-dimensional vector space where dissimilarity is measured using the Euclidean distance, Manhattan

theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. A common proof identifies the unit

theorem can be generalized from Banach spaces to more abstract topological vector spaces in the following ways. Theorem—A linear operator from a barrelled

in which the morphisms fij are surjective a system of finite-dimensional vector spaces or finite abelian groups or modules of finite length or Artinian

The special case of calculus in three dimensional space is often called vector calculus. In single-variable calculus, operations like differentiation and

pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can

graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization

arrays can be called a vectorized operation, regardless of whether it is executed on a vector processor, which implements vector instructions. Array programming

Vector Limited is a New Zealand energy company, which runs a portfolio of businesses delivering energy and communication services across Australasia and

linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator

can define the trace of a linear operator mapping a finite-dimensional vector space into itself, since all matrices describing such an operator with respect

is a column vector describing the position of a point in space, the product R v {\displaystyle R\mathbf {v} } yields another column vector describing the

Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R 2

any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless, linear

to be injective. For some types of structure, such as abelian groups and vector spaces, the possible kernels are exactly the substructures of the same type

polyhedron. A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)

Microsoft, and Visio; the note contained a draft specification for the Vector Markup Language (VML), another XML-based markup language. As a result of

Organization (WHO) guidelines from the ban. DDT still has limited use in disease vector control because of its effectiveness in killing mosquitos and thus reducing

spacetime, predicted by general relativity, on a vector carried along with an orbiting body. For example, the vector could be the angular momentum of a gyroscope

Scientists theorized that a virus could also be used as a vehicle, or vector, to deliver new genes into cells. One of the first scientists to report