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Vanishing point (1,858 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 parallel lines in three-dimensional

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

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

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

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

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;

Lorentz force (8,525 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 (692 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 (5,011 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

Lagrange's identity (3,679 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) (1,218 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

History of special relativity (16,903 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

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

Ponderomotive force (2,327 words) [view diff] exact match in snippet view article find links to article

general fields, the starting point is the exact equations, in four-vector notation: m d u μ d τ = R e [ f μ ] = R e [ f ^ μ ( x , u ) e − i k ν x ν ]

Pair production (1,392 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 (964 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 (1,496 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 (2,248 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 (2,825 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

Richard M. Friedberg (945 words) [view diff] exact match in snippet view article find links to article

been reviewed by Friedberg who translated the work, provided modern vector notation, diagrams, and annotation of the text. 1957: (communicated by Kurt

Numerical algebraic geometry (1,306 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

Partial trace (2,121 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 \{\vert \ell \rangle \}_{\ell }} ⁠

Delta method (2,415 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) =

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

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 [

Triple product (3,621 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

Euler–Rodrigues formula (2,423 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\vec {\omega }}=(b,c,d)} the vector parameter. In standard vector notation, the Rodrigues rotation formula takes the compact form[citation needed]

Circumflex (3,826 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

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

Larmor formula (2,469 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

Degrees of freedom (statistics) (4,530 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

Lagrangian mechanics (14,700 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

Long short-term memory (5,788 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}}

Covariant formulation of classical electromagnetism (4,014 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

Coulomb's law (6,652 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

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

Ordinary differential equation (5,187 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

Viscosity (11,463 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

Centrality (6,738 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 (9,524 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 (1,578 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 (13,704 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 (11,568 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 ∑

Regularized least squares (4,894 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

First-order partial differential equation (3,130 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 (8,234 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 (2,086 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

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

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 ) , … , (

Rigid rotor (6,099 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 Laplace operator (5,716 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

Discrete Fourier transform (12,333 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

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

Logistic regression (20,645 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

Electron scattering (5,071 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

Adiabatic theorem (4,537 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

Relativistic angular momentum (10,985 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

List of textbooks on relativity (1,156 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

Euler equations (fluid dynamics) (13,150 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

List of autodidacts (8,589 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

Singular integral operators on closed curves (5,037 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

History of Lorentz transformations (15,399 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 ′ =

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

Neumann–Poincaré operator (11,017 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