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searching for Vector notation 71 found (93 total)

Vanishing point (1,859 words) [view diff] no match in snippet view article find links to article

A vanishing point is a point on the image plane of a perspective rendering where the two-dimensional perspective projections of mutually parallel lines

Hesse normal form (590 words) [view diff] exact match in snippet view article find links to article

(see point-plane distance and point-line distance). It is written in vector notation as r → ⋅ n → 0 − d = 0. {\displaystyle {\vec {r}}\cdot {\vec {n}}_{0}-d=0

Rotational–vibrational coupling (1,551 words) [view diff] exact match in snippet view article find links to article

the period of the overall motion. As expected, the analysis using vector notation results in a straight confirmation of the previous analysis: The spring

Geometrical optics (4,688 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varepsilon } and μ {\displaystyle \mu } . In four-vector notation used in special relativity, the wave equation can be written as ∂ 2

Vectors in Three-dimensional Space (284 words) [view diff] exact match in snippet view article find links to article

in two different ways: in a wide variety of physical applications, vector notation and techniques became, by the middle of this century, almost universal;

Linear predictor function (2,134 words) [view diff] no match in snippet view article find links to article

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables

Lorentz force (8,418 words) [view diff] exact match in snippet view article find links to article

half in front of the formula. Oliver Heaviside invented the modern vector notation and applied it to Maxwell's field equations; he also (in 1885 and 1889)

Hawkins–Simon condition (680 words) [view diff] exact match in snippet view article find links to article

is the amount of final demand for good i. Rearranged and written in vector notation, this gives the first equation. Define [ I − A ] = B {\displaystyle

Frenet–Serret formulas (4,980 words) [view diff] exact match in snippet view article find links to article

Frenet, in his thesis of 1847, and Joseph Alfred Serret, in 1851. Vector notation and linear algebra currently used to write these formulas were not

History of special relativity (16,643 words) [view diff] exact match in snippet view article find links to article

electrodynamics, even though it was later replaced by Sommerfeld using vector notation. According to a recent source the Lorentz transformations are equivalent

Lagrange's identity (3,678 words) [view diff] exact match in snippet view article find links to article

and a special form of the Binet–Cauchy identity. In a more compact vector notation, Lagrange's identity is expressed as: ‖ a ‖ 2 ‖ b ‖ 2 − ( a ⋅ b ) 2

Dilution (neural networks) (1,216 words) [view diff] exact match in snippet view article

x_{j}} – input from node j {\displaystyle j} This can be written in vector notation as y {\displaystyle \mathbf {y} } – output vector W {\displaystyle

Bloch equations (3,276 words) [view diff] exact match in snippet view article find links to article

{dM_{z}(t)}{dt}}=\gamma (\mathbf {M} (t)\times \mathbf {B} (t))_{z}} or, in vector notation: d M ( t ) d t = γ M ( t ) × B ( t ) {\displaystyle {\frac {d\mathbf

Josef Stefan (897 words) [view diff] exact match in snippet view article find links to article

Very important are also his electromagnetic equations, defined in vector notation, and works in the kinetic theory of heat. Stefan was among the first

History of Maxwell's equations (3,945 words) [view diff] exact match in snippet view article find links to article

grouped the twenty equations together into a set of only four, via vector notation. This group of four equations was known variously as the Hertz–Heaviside

Hydraulic head (1,863 words) [view diff] exact match in snippet view article find links to article

(length, usually in m or ft) The hydraulic gradient can be expressed in vector notation, using the del operator. This requires a hydraulic head field, which

Pair production (1,390 words) [view diff] exact match in snippet view article find links to article

can be derived through the kinematics of the interaction. Using four vector notation, the conservation of energy–momentum before and after the interaction

Perl Data Language (971 words) [view diff] exact match in snippet view article find links to article

language: the expression syntax is a variation on standard mathematical vector notation, so that the user can combine and operate on large arrays with simple

Lorenz gauge condition (1,450 words) [view diff] exact match in snippet view article find links to article

It still leaves substantial gauge degrees of freedom. In ordinary vector notation and SI units, the condition is ∇ ⋅ A + 1 c 2 ∂ φ ∂ t = 0 , {\displaystyle

EIO-LCA (1,287 words) [view diff] exact match in snippet view article find links to article

∑ j A i j x j {\displaystyle x_{i}=y_{i}+\sum _{j}A_{ij}x_{j}} In vector notation x = y + A x {\displaystyle \mathbf {x} =\mathbf {y} +\mathbf {Ax} }

Surface integral (2,251 words) [view diff] exact match in snippet view article find links to article

This formula defines the integral on the left (note the dot and the vector notation for the surface element). We may also interpret this as a special case

Eigenvector centrality (1,340 words) [view diff] exact match in snippet view article find links to article

is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation A x = λ x {\displaystyle \mathbf {Ax} =\lambda

Daubechies wavelet (2,806 words) [view diff] exact match in snippet view article find links to article

periodization is accomplished in the forward transform directly in MATLAB vector notation, and the inverse transform by using the circshift() function: It is

Four-velocity (1,711 words) [view diff] exact match in snippet view article find links to article

{\begin{bmatrix}c\\{\vec {u}}\\\end{bmatrix}}.} Written in standard four-vector notation this is: U = γ ( c , u → ) = ( γ c , γ u → ) {\displaystyle \mathbf

Triple product (3,014 words) [view diff] exact match in snippet view article find links to article

{e} &\mathbf {c} \cdot \mathbf {f} \end{bmatrix}}} This restates in vector notation that the product of the determinants of two 3×3 matrices equals the

Numerical algebraic geometry (1,283 words) [view diff] exact match in snippet view article find links to article

ambient spaces over which one can solve the system, we do not use vector notation for z {\displaystyle z} . Similarly for the polynomial systems f {\displaystyle

Euler–Rodrigues formula (2,052 words) [view diff] exact match in snippet view article find links to article

scalar parameter and ω→ = (b, c, d) the vector parameter. In standard vector notation, the Rodrigues rotation formula takes the compact form[citation needed]

Partial trace (2,047 words) [view diff] exact match in snippet view article find links to article

defined. Suppose W has an orthonormal basis, which we denote by ket vector notation as { | ℓ ⟩ } ℓ {\displaystyle \{|\ell \rangle \}_{\ell }} . Then Tr

Delta method (2,413 words) [view diff] exact match in snippet view article find links to article

Keeping only the first two terms of the Taylor series, and using vector notation for the gradient, we can estimate h(B) as h ( B ) ≈ h ( β ) + ∇ h (

Real projective plane (2,704 words) [view diff] exact match in snippet view article find links to article

above can be written in matrix form as: xTℓ = 0 or ℓTx = 0. Using vector notation we may instead write x ⋅ ℓ = 0 or ℓ ⋅ x = 0. The equation k(xTℓ) =

Levenberg–Marquardt algorithm (3,211 words) [view diff] exact match in snippet view article find links to article

}}\right)-\mathbf {J} _{i}{\boldsymbol {\delta }}\right]^{2},} or in vector notation, S ( β + δ ) ≈ ‖ y − f ( β ) − J δ ‖ 2 = [ y − f ( β ) − J δ ] T [

Hooke's law (9,420 words) [view diff] exact match in snippet view article find links to article

_{33}\\2\varepsilon _{23}\\2\varepsilon _{13}\\2\varepsilon _{12}\end{bmatrix}}} In vector notation this becomes [ σ 11 σ 12 σ 13 σ 12 σ 22 σ 23 σ 13 σ 23 σ 33 ] = 2 μ

Acorn System BASIC (3,487 words) [view diff] exact match in snippet view article find links to article

string. This concept allows individual characters to be accessed using vector notation. For instance, A?5 would return the ASCII value of the 5th character

Circumflex (3,823 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\hat {A}}} or A B C ^ {\displaystyle {\widehat {ABC}}} . In vector notation, a hat above a letter indicates a unit vector (a dimensionless vector

Degrees of freedom (statistics) (4,540 words) [view diff] exact match in snippet view article

{X}}+{\bar {Y}}+{\bar {Z}})/3} is the mean of all 3n observations. In vector notation this decomposition can be written as ( X 1 ⋮ X n Y 1 ⋮ Y n Z 1 ⋮ Z

Larmor formula (2,456 words) [view diff] exact match in snippet view article find links to article

}}{d\tau }}.} To show this, we reduce the four-vector scalar product to vector notation. We start with d p μ d τ d p μ d τ = γ 2 [ ( d p 0 d t ) 2 − ( d p

Lagrangian mechanics (14,505 words) [view diff] exact match in snippet view article find links to article

particle of constant mass m is Newton's second law of 1687, in modern vector notation F = m a , {\displaystyle \mathbf {F} =m\mathbf {a} ,} where a is its

Covariant formulation of classical electromagnetism (3,929 words) [view diff] exact match in snippet view article find links to article

{\mathcal {D}}^{\mu \nu }} can be derived. The equivalent expression in vector notation is: L = 1 2 ( ε 0 E 2 − 1 μ 0 B 2 ) − ϕ ρ free + A ⋅ J free + E ⋅ P

Long short-term memory (5,782 words) [view diff] exact match in snippet view article find links to article

activation being calculated. In this section, we are thus using a "vector notation". So, for example, c t ∈ R h {\displaystyle c_{t}\in \mathbb {R} ^{h}}

Coulomb's law (6,645 words) [view diff] exact match in snippet view article find links to article

Here, r ^ 12 {\textstyle \mathbf {\hat {r}} _{12}} is used for the vector notation. The electrostatic force F 2 {\textstyle \mathbf {F} _{2}} experienced

Ordinary differential equation (5,222 words) [view diff] exact match in snippet view article find links to article

y_{1},\ldots ,y_{n}).\end{array}}} more compactly in vector notation: y ′ = F ( x , y ) {\displaystyle \mathbf {y} '=\mathbf {F} (x,\mathbf

Kerr–Newman metric (4,780 words) [view diff] exact match in snippet view article find links to article

tensor. It will be convenient to switch over to three-dimensional vector notation. A μ = ( − ϕ , A x , A y , A z ) {\displaystyle A_{\mu }=\left(-\phi

Viscosity (11,449 words) [view diff] exact match in snippet view article find links to article

{2}{3}}\mu } and β = γ = μ {\displaystyle \beta =\gamma =\mu } . In vector notation this appears as: τ = μ [ ∇ v + ( ∇ v ) T ] − ( 2 3 μ − κ ) ( ∇ ⋅ v

Regularized least squares (4,273 words) [view diff] exact match in snippet view article find links to article

_{i=1}^{n}c_{i}K(x_{i},x_{*})=K(X,X_{*})^{\mathsf {T}}c} For convenience a vector notation is introduced. Let X {\displaystyle X} be an n × d {\displaystyle n\times

Centrality (6,733 words) [view diff] exact match in snippet view article find links to article

is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation A x = λ x {\displaystyle \mathbf {Ax} ={\lambda

Calculus of variations (9,282 words) [view diff] exact match in snippet view article find links to article

first variation of the optical path length. It is expedient to use vector notation: let X = ( x 1 , x 2 , x 3 ) , {\displaystyle X=(x_{1},x_{2},x_{3})

List of pioneers in computer science (1,564 words) [view diff] exact match in snippet view article find links to article

Calculation with Hindu Numerals. 1970, 1989 Allen, Frances E. Developed bit vector notation and program control-flow graphs; first female IBM Fellow (1989); first

ARM architecture family (13,701 words) [view diff] exact match in snippet view article find links to article

coprocessor". ARM.com. Retrieved 20 August 2014. "VFP directives and vector notation". ARM.com. Retrieved 21 November 2011. "Differences between ARM Cortex-A8

Cross product (11,474 words) [view diff] exact match in snippet view article find links to article

tensor Eijk and a dot product ηmi, which are useful in converting vector notation for tensor applications: c = a × b ⇔ c m = ∑ i = 1 3 ∑ j = 1 3 ∑

First-order partial differential equation (3,124 words) [view diff] exact match in snippet view article find links to article

{\displaystyle u_{x}^{2}+u_{y}^{2}+u_{z}^{2}={\frac {1}{c^{2}}}.\,} In vector notation, let x → = ( x , y , z ) and p → = ( u x , u y , u z ) . {\displaystyle

Linear elasticity (8,230 words) [view diff] exact match in snippet view article find links to article

the steady Navier–Cauchy equations, which can be also expressed in vector notation as ( λ + μ ) ∇ ( ∇ ⋅ u ) + μ ∇ 2 u + F = 0 {\displaystyle (\lambda

Meta-regression (2,080 words) [view diff] exact match in snippet view article find links to article

xtk′β + γtk + εtk. The advantage of writing the model in a matrix-vector notation is that the correlation between the treatments, Corr(γ1k, γ2k), can

Meijer G-function (10,023 words) [view diff] exact match in snippet view article find links to article

argument of the hypergeometric function, if we recall the meaning of the vector notation, 1 + b h − b q = ( 1 + b h − b 1 ) , … , ( 1 + b h − b j ) , … , (

Synchronous coefficient of drag alteration (2,152 words) [view diff] exact match in snippet view article find links to article

{dv_{y_{cos2\omega }}}}=-{\frac {kEdE_{q}}{4}}y} (17) which can be summarized in vector notation to: d v → ¯ = − k E d E q 4 r → {\displaystyle {\bar {d{\overrightarrow

Discrete Laplace operator (5,719 words) [view diff] exact match in snippet view article find links to article

_{j}\\&=-k\sum _{j}\left(L_{ij}\right)\phi _{j}.\end{aligned}}} In matrix-vector notation, d ϕ d t = − k ( D − A ) ϕ = − k L ϕ , {\displaystyle {\begin{aligned}{\frac

Rigid rotor (6,088 words) [view diff] exact match in snippet view article find links to article

a function of the time derivatives of the Euler angles). In matrix-vector notation, 2 T = ( α ˙ β ˙ γ ˙ ) g ( α ˙ β ˙ γ ˙ ) , {\displaystyle 2T={\begin{pmatrix}{\dot

Discrete Fourier transform (12,371 words) [view diff] exact match in snippet view article find links to article

k_{\ell }=0,1,\dots ,N_{\ell }-1} . This is more compactly expressed in vector notation, where we define n = ( n 1 , n 2 , … , n d ) {\displaystyle \mathbf

Logistic regression (20,643 words) [view diff] exact match in snippet view article find links to article

_{m=0}^{M}(\lambda _{n'm}x_{mk'})-\alpha _{k'}} Using the more condensed vector notation: ∑ m = 0 M λ n m x m k = λ n ⋅ x k {\displaystyle \sum _{m=0}^{M}\lambda

Financial contagion (5,053 words) [view diff] exact match in snippet view article find links to article

stocks v {\displaystyle v} and v ′ {\displaystyle v^{\prime }} . In vector notation, the standard model for contagion tests can be written as a VAR (vector

Electron scattering (5,055 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F={\frac {|q_{1}q_{2}|}{4\pi \epsilon _{0}r^{2}}}} or in vector notation: F = q 1 q 2 4 π ϵ 0 | r | 2 r ^ {\displaystyle {\boldsymbol {F}}={\frac

List of textbooks on relativity (1,110 words) [view diff] exact match in snippet view article find links to article

Saha, "Space and Time" (1920): Wikisource link. : Introduced the four-vector notation and the notion of Minkowski space, which was later adopted by Einstein

Relativistic angular momentum (10,805 words) [view diff] exact match in snippet view article find links to article

^{k}\beta _{i}\varepsilon ^{\ell in}L_{n}\right)\\\end{aligned}}} in vector notation L ′ = γ c β × N + L + γ − 1 β 2 β × ( β × L ) {\displaystyle \mathbf

Adiabatic theorem (4,538 words) [view diff] exact match in snippet view article find links to article

_{m})-i(\gamma _{m}-\gamma _{n})}d\lambda \end{aligned}}} or written in vector notation d → ( 1 ) − d → ( 0 ) = − ∫ 0 1 A ^ ( T , λ ) ( d → ( λ ) − d → ( 0

Euler equations (fluid dynamics) (13,178 words) [view diff] exact match in snippet view article

in the so-called conservation (or Eulerian) differential form, with vector notation: { ∂ u ∂ t + ∇ ⋅ ( u ⊗ u + w I ) = 0 ∂ 0 ∂ t + ∇ ⋅ u = 0 , {\displaystyle

Analytical Dynamics of Particles and Rigid Bodies (5,645 words) [view diff] exact match in snippet view article find links to article

tendency to make things more complicated than necessary, refusal to use vector notation, and "pedantic" problems of the kind found on the Cambridge Tripos

Singular integral operators on closed curves (5,028 words) [view diff] exact match in snippet view article find links to article

the level curves in a tubular neighbourhood of the boundary. Using vector notation v(t) = (x(t), y(t)) to parametrize the boundary curve by arc length

List of autodidacts (8,532 words) [view diff] exact match in snippet view article find links to article

to solve differential equations, expressed Maxwell's equations in vector notation, and made significant contributions to transmission line theory. He

A History of the Theories of Aether and Electricity (10,506 words) [view diff] exact match in snippet view article find links to article

explanatory table at the beginning of the book for those unfamiliar with vector notation. The first chapter covers the 17th-century development of the theory

History of Lorentz transformations (15,389 words) [view diff] exact match in snippet view article find links to article

{1-v^{2}}}}\end{aligned}}\end{matrix}}} This was simplified using vector notation by Ludwik Silberstein (1911 on the left, 1914 on the right): r ′ =

Neumann–Poincaré operator (11,016 words) [view diff] exact match in snippet view article find links to article

diagonal but it admit a (unique) smooth extension to the diagonal. Using vector notation v(t) = (x(t), y(t)) to parametrize the boundary curve by arc length

Adaptive noise cancelling (4,165 words) [view diff] exact match in snippet view article find links to article

and the desired response: where W represents the set of weights in vector notation and X(t) the set of weight inputs so y(t) = X(t)TW. The above expression