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Find link is a tool written by Edward Betts.Longer titles found: Anti-diagonal matrix (view), Tridiagonal matrix (view)
searching for Diagonal matrix 169 found (337 total)
alternate case: diagonal matrix
Slater–Condon rules
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interaction theories. In 1929 John C. Slater derived expressions for diagonal matrix elements of an approximate Hamiltonian while investigating atomic spectraM-matrix (1,173 words) [view diff] exact match in snippet view article find links to article
positive diagonal matrix D such that AD has all positive row sums. A has all positive diagonal elements, and there exists a positive diagonal matrix D suchCrout matrix decomposition (363 words) [view diff] exact match in snippet view article find links to article
is such that: A = LDU being L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method producesEigenvalues and eigenvectors (13,539 words) [view diff] exact match in snippet view article find links to article
{\displaystyle D:=V^{T}AV} , we get a matrix whose top left block is the diagonal matrix λ I γ A ( λ ) {\displaystyle \lambda I_{\gamma _{A}(\lambda )}} . ThisNullity (graph theory) (318 words) [view diff] exact match in snippet view article
Laplacian matrix of the graph, defined as L = D − A, where D is the diagonal matrix of vertex degrees; the Laplacian nullity equals the cycle rank becauseJordan matrix (2,805 words) [view diff] exact match in snippet view article find links to article
matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities are the zero 0 and one 1), where eachSquare root of a 2 by 2 matrix (1,254 words) [view diff] no match in snippet view article find links to article
A square root of a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there canBauer–Fike theorem (1,640 words) [view diff] exact match in snippet view article find links to article
non-singular eigenvector matrix such that A = VΛV −1, where Λ is a diagonal matrix. If X ∈ Cn,n is invertible, its condition number in p-norm is denotedDrazin inverse (740 words) [view diff] exact match in snippet view article find links to article
A D = A − 1 {\displaystyle A^{\text{D}}=A^{-1}} . If A is a block diagonal matrix A = [ B 0 0 N ] {\displaystyle A={\begin{bmatrix}B&0\\0&N\end{bmatrix}}}Kirchhoff's theorem (2,035 words) [view diff] exact match in snippet view article find links to article
which is equal to the difference between the graph's degree matrix (a diagonal matrix with vertex degrees on the diagonals) and its adjacency matrix (a (0Reducing subspace (421 words) [view diff] exact match in snippet view article find links to article
{\displaystyle Q^{-1}MQ} representing T {\displaystyle T} is a block-diagonal matrix Q − 1 M Q = [ A 0 0 B ] {\displaystyle Q^{-1}MQ=\left[{\begin{arraBregman–Minc inequality (917 words) [view diff] exact match in snippet view article find links to article
is a block diagonal matrix consisting of matrices of ones or results from row and/or column permutations of such a block diagonal matrix. Since the permanentIterative proportional fitting (3,464 words) [view diff] exact match in snippet view article find links to article
as a zero in X {\displaystyle X} . Thus, a bloc-diagonal matrix is projected as a bloc-diagonal matrix and a triangular matrix is projected as a triangularJacobi eigenvalue algorithm (3,928 words) [view diff] exact match in snippet view article find links to article
by a factor ( 1 − 1 / N ) 1 / 2 {\displaystyle (1-1/N)^{1/2}} to a diagonal matrix. A number of N {\displaystyle N} Jacobi rotations is called a sweep;Chromatic adaptation (1,061 words) [view diff] exact match in snippet view article find links to article
2}/L_{1}&0&0\\0&M_{2}/M_{1}&0\\0&0&S_{2}/S_{1}\end{bmatrix}}} This diagonal matrix D maps cone responses, or colors, in one adaptation state to correspondingSchur–Horn theorem (2,888 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\tilde {\lambda }}.} Let Λ {\displaystyle \Lambda } be the diagonal matrix having λ 1 , λ 2 , … , λ n {\displaystyle \lambda _{1},\lambda _{2}Compact finite difference (1,122 words) [view diff] exact match in snippet view article find links to article
disadvantage is that compact schemes are implicit and require to solve a diagonal matrix system for the evaluation of interpolations or derivatives at all gridPolar decomposition (4,173 words) [view diff] exact match in snippet view article find links to article
equivalent to a diagonal matrix: A = V Λ V ∗ {\displaystyle A=V\Lambda V^{*}} for some unitary matrix V {\displaystyle V} and some diagonal matrix Λ {\displaystyleCorner transfer matrix (2,357 words) [view diff] exact match in snippet view article find links to article
ordering the configurations appropriately we may cast A as a block diagonal matrix: σ 1 ′ = + 1 σ 1 ′ = − 1 A = [ | A + | 0 | − − − | − − − | 0 | A −Fractional Brownian motion (2,157 words) [view diff] exact match in snippet view article find links to article
{\displaystyle i=1,\dots ,n} ). Let Λ {\displaystyle \,\Lambda } be the diagonal matrix of the eigenvalues, i.e. Λ i j = λ i δ i j {\displaystyle \Lambda _{ij}=\lambdaLimited-memory BFGS (2,370 words) [view diff] exact match in snippet view article find links to article
approximate inverse Hessian H k 0 {\displaystyle H_{k}^{0}} is chosen as a diagonal matrix or even a multiple of the identity matrix since this is numericallyDiffusion map (2,371 words) [view diff] exact match in snippet view article find links to article
L(α)=D−αLD−α{\displaystyle L^{(\alpha )}=D^{-\alpha }LD^{-\alpha }\,} where D is a diagonal matrix and Di,i=∑jLi,j.{\displaystyle D_{i,i}=\sum _{j}L_{i,j}.} We applyQuantum statistical mechanics (1,233 words) [view diff] exact match in snippet view article find links to article
possible that H(S) = +∞ for some density operator S. In fact T be the diagonal matrix T=[12(log22)20⋯0⋯013(log23)2⋯0⋯⋮⋮⋱001n(log2n)2⋮⋮⋱]{\displaystyleFrobenius group (1,272 words) [view diff] exact match in snippet view article find links to article
The Frobenius complement H is the cyclic subgroup generated by the diagonal matrix whose i,i'th entry is zi. The Frobenius kernel K is the Sylow q-subgroupSignature (topology) (767 words) [view diff] exact match in snippet view article
that is, σ(M)=n+−n−{\displaystyle \sigma (M)=n_{+}-n_{-}} where any diagonal matrix defining Q has n+{\displaystyle n_{+}} positive entries and n−{\displaystyleTrust region (735 words) [view diff] exact match in snippet view article find links to article
x=b}, where diag(A){\displaystyle \operatorname {diag} (A)} is the diagonal matrix with the same diagonal as A, and λ is a parameter that controls thePrincipal curvature (1,290 words) [view diff] exact match in snippet view article find links to article
the matrix [ I I i j ] {\displaystyle \left[I\!I_{ij}\right]} is a diagonal matrix, then they are called the principal directions. If the surface is orientedGeneralized chi-squared distribution (1,784 words) [view diff] exact match in snippet view article find links to article
{T} }z=(x+b)^{\mathrm {T} }D(x+b)+d^{\mathrm {T} }x+e,} where D is a diagonal matrix and where x represents a vector of uncorrelated standard normal randomMatrix addition (1,208 words) [view diff] exact match in snippet view article find links to article
matrix. In particular, the direct sum of square matrices is a block diagonal matrix. The adjacency matrix of the union of disjoint graphs (or multigraphs)Frequency domain decomposition (308 words) [view diff] exact match in snippet view article find links to article
vectors u i j {\displaystyle u_{ij}} , S i {\displaystyle S_{i}} is the diagonal matrix holding the singular values s i j {\displaystyle s_{ij}} . For an nEstimation of signal parameters via rotational invariance techniques (4,021 words) [view diff] exact match in snippet view article find links to article
T} , respectively. E {\textstyle \mathbf {E} } is a non-rectangular diagonal matrix of size M × T {\textstyle M\times T} that holds the singular valuesCarrier interferometry (1,628 words) [view diff] exact match in snippet view article find links to article
= F−1ΛHF is from the definition of a circulant matrix, and ΛH is a diagonal matrix whose diagonal elements correspond to the first column of the circulantProto-value function (1,034 words) [view diff] exact match in snippet view article find links to article
operator L=D−A{\displaystyle L=D-A}, where D{\displaystyle D} is a diagonal matrix called the degree matrix and A{\displaystyle A} is the adjacency matrixHeat kernel signature (2,356 words) [view diff] exact match in snippet view article find links to article
{\displaystyle L=A^{-1}W} where A {\displaystyle A} is a positive diagonal matrix with entries A ( i , i ) {\displaystyle A(i,i)} corresponding to theStress (mechanics) (5,558 words) [view diff] exact match in snippet view article
2 , e 3 {\displaystyle e_{1},e_{2},e_{3}} , the stress tensor is a diagonal matrix, and has only the three normal components λ 1 , λ 2 , λ 3 {\displaystyleDirichlet's ellipsoidal problem (1,769 words) [view diff] exact match in snippet view article find links to article
_{j=1}^{3}P_{ij}(t){\frac {x_{j}(0)}{a_{j}(0)}}.} and we define a diagonal matrix A ( t ) {\displaystyle \mathbf {A} (t)} with diagonal elements beingSpecial linear group (1,472 words) [view diff] exact match in snippet view article find links to article
sequence splits by taking any matrix with determinant −1, for example the diagonal matrix ( − 1 , 1 , … , 1 ) . {\displaystyle (-1,1,\dots ,1).} If n = 2 k +Durand–Kerner method (3,079 words) [view diff] exact match in snippet view article find links to article
TAT^{-1}} of A is as well a companion matrix of ƒ(X). Choosing T as diagonal matrix leaves the structure of A invariant. The root close to z k {\displaystyleConfidence region (1,261 words) [view diff] exact match in snippet view article find links to article
proportional to the reciprocals of the values on the diagonals of the diagonal matrix, and the directions of these axes are given by the rows of the 3rdGivens rotation (2,514 words) [view diff] exact match in snippet view article find links to article
Another method can extend Givens rotations to complex matrices. A diagonal matrix whose diagonal elements have unit magnitudes but arbitrary phases is(B, N) pair (986 words) [view diff] exact match in snippet view article
represented by the matrices obtained by swapping two adjacent rows of a diagonal matrix. The Weyl group is the symmetric group on n letters. More generallyRV coefficient (769 words) [view diff] exact match in snippet view article find links to article
ΛX{\displaystyle \Lambda _{X}} (resp. ΛY{\displaystyle \Lambda _{Y}}) denotes the diagonal matrix of the eigenvalues of ΣXX{\displaystyle \Sigma _{XX}}(resp. ΣYY{\displaystyleEckart conditions (3,018 words) [view diff] exact match in snippet view article find links to article
_{1}^{0},\ldots ,\mathbf {R} _{N}^{0}}. The diagonal matrix M contains the masses on the diagonal. The diagonal matrix Φ{\displaystyle {\boldsymbol {\Phi }}}Oscillator strength (1,121 words) [view diff] exact match in snippet view article find links to article
omitted because in confined systems such as atoms or molecules the diagonal matrix element ⟨n|px|n⟩=0{\displaystyle \langle n|p_{x}|n\rangle =0} due toSchrieffer–Wolff transformation (2,124 words) [view diff] exact match in snippet view article find links to article
its diagonal, to transform H 0 {\displaystyle H_{0}} into a purely diagonal matrix D 0 = diag ( d i ) {\displaystyle D_{0}=\operatorname {diag} (d_{i})}Eigenstate thermalization hypothesis (5,544 words) [view diff] exact match in snippet view article find links to article
off-diagonal matrix elements A α β {\displaystyle A_{\alpha \beta }} , with α ≠ β {\displaystyle \alpha \neq \beta } , are much smaller than the diagonalSchmidt decomposition (1,210 words) [view diff] exact match in snippet view article find links to article
ρ{\displaystyle \rho }, with respect to either system A or B, is a diagonal matrix whose non-zero diagonal elements are |αi|2{\displaystyle |\alpha _{i}|^{2}}Semisimple Lie algebra (5,731 words) [view diff] exact match in snippet view article find links to article
a 1 , … , a n ) {\displaystyle d(a_{1},\ldots ,a_{n})} denotes the diagonal matrix with a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} on the diagonalBorn–Oppenheimer approximation (5,075 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \chi _{k}} can be chosen to be always real. The off-diagonal matrix elements satisfy ⟨ χ k ′ | P A α | χ k ⟩ ( r ) = ⟨ χ k ′ | [ P A αEigenvector centrality (1,340 words) [view diff] exact match in snippet view article find links to article
d i a g ( x ) {\displaystyle \mathbf {diag} (\mathbf {x} )} is the diagonal matrix of vector x {\displaystyle \mathbf {x} } . N {\displaystyle \mathbfCayley transform (2,136 words) [view diff] exact match in snippet view article find links to article
Q=E(I-A)(I+A)^{-1}} for some skew-symmetric matrix A and some diagonal matrix E with ±1 as entries. A slightly different form is also seen, requiringMaximal torus (1,734 words) [view diff] exact match in snippet view article find links to article
\mathrm {diag} \left(e^{i\theta },e^{-i\theta }\right)} denotes the diagonal matrix with diagonal entries e i θ {\displaystyle e^{i\theta }} and e − iPerron–Frobenius theorem (8,235 words) [view diff] exact match in snippet view article find links to article
invertible then neither is PAP−1 or A. Conversely let D be the block-diagonal matrix corresponding to PAP−1, in other words PAP−1 with the asterisks zeroisedMultiple correspondence analysis (1,655 words) [view diff] exact match in snippet view article find links to article
unitary matrices and Δ {\displaystyle \Delta } is the generalized diagonal matrix of the singular values (with the same shape as Z {\displaystyle Z}Transition dipole moment (1,421 words) [view diff] exact match in snippet view article find links to article
other words, the transition dipole moment can be viewed as an off-diagonal matrix element of the position operator, multiplied by the particle's chargeVirtual fixture (2,426 words) [view diff] exact match in snippet view article find links to article
slave robot. If the constant c {\displaystyle c} is replaced by a diagonal matrix C {\displaystyle \mathbf {C} } it is possible to adjust the complianceSolvable group (3,073 words) [view diff] exact match in snippet view article find links to article
with d = − b / a {\displaystyle d=-b/a} , we can get a diagonal matrix in B {\displaystyle B} . This shows the quotient group B / U ≅ F ×Zero-forcing precoding (1,384 words) [view diff] exact match in snippet view article find links to article
Q{\displaystyle \mathbf {Q} } is some K×K{\displaystyle K\times K} diagonal matrix. Typically, Q{\displaystyle \mathbf {Q} } is selected to be an identityWalk-regular graph (519 words) [view diff] exact match in snippet view article find links to article
{\displaystyle G} is walk-regular. A k {\displaystyle A^{k}} is a constant-diagonal matrix for all k ≥ 0. {\displaystyle k\geq 0.} Φ G − u ( x ) = Φ G − v ( xSPIKE algorithm (3,549 words) [view diff] exact match in snippet view article find links to article
blocks Aj (j = 1,...,p with p ≥ 2) are nonsingular. Define a block diagonal matrix D = diag(A1,...,Ap), then D is also nonsingular. Left-multiplying D−1Segmentation-based object categorization (1,816 words) [view diff] exact match in snippet view article find links to article
\limits _{j}w_{ij}} Also, let D be an n×n{\displaystyle n\times n} diagonal matrix with d{\displaystyle d} on the diagonal, and let W{\displaystyle W}FastICA (1,241 words) [view diff] exact match in snippet view article find links to article
the matrix of eigenvectors and D {\displaystyle \mathbf {D} } is the diagonal matrix of eigenvalues. The whitened data matrix is defined thus by X ← D −Factor analysis (10,026 words) [view diff] exact match in snippet view article find links to article
will be 1 {\displaystyle 1} s. The second term on the right will be a diagonal matrix with terms less than unity. The first term on the right is the "reducedSmoothing spline (2,306 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \Delta _{i,i+2}=1/h_{i+1}} W is an (n-2)×(n-2) symmetric tri-diagonal matrix with elements: W i − 1 , i = W i , i − 1 = h i / 6 {\displaystyle W_{i-1Stress–energy tensor (3,996 words) [view diff] exact match in snippet view article find links to article
\\0&0&0&1\end{matrix}}\right)\,} and the stress–energy tensor is a diagonal matrix T α β = ( ρ 0 0 0 0 p 0 0 0 0 p 0 0 0 0 p ) . {\displaystyle T^{\alphaRabi frequency (2,160 words) [view diff] exact match in snippet view article find links to article
|i⟩{\displaystyle |i\rangle } of the Hydrogen atom potential, the diagonal matrix elements go to zero, leaving us with ic˙1(t)=c2(t)cos(ωt)ℏ⟨1|er⋅ELevenberg–Marquardt algorithm (3,211 words) [view diff] exact match in snippet view article find links to article
replacing the identity matrix I {\displaystyle \mathbf {I} } with the diagonal matrix consisting of the diagonal elements of J T J {\displaystyle \mathbfNeuromorphic engineering (4,641 words) [view diff] exact match in snippet view article find links to article
memristor; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector X = diag ( X → ) {\displaystyle X=\operatorname {diag}Touchscreen (12,942 words) [view diff] exact match in snippet view article find links to article
simplify this process. By slightly distorting the conductors in a "n" I/O diagonal matrix, the equivalent of a (n-1) by (n/2) array is formed. After addressCyclotomic fast Fourier transform (1,228 words) [view diff] exact match in snippet view article find links to article
aijs{\displaystyle a_{ijs}}, L{\displaystyle \mathbf {L} } is a block diagonal matrix, and Π{\displaystyle \mathbf {\Pi } } is a permutation matrix regroupingRayleigh–Ritz method (2,840 words) [view diff] exact match in snippet view article find links to article
matrix U {\displaystyle \mathbf {U} } , m × m {\displaystyle m\times m} diagonal matrix Σ {\displaystyle \Sigma } , and m × m {\displaystyle m\times m} matrixT-symmetry (4,234 words) [view diff] exact match in snippet view article find links to article
Z2 symmetry generator T2 = UKUK = UU* = U (UT)−1 = Φ, where Φ is a diagonal matrix of phases. As a result, U = ΦUT and UT = UΦ, showing that U = Φ U ΦOverdetermined system (2,206 words) [view diff] exact match in snippet view article find links to article
matrix A {\displaystyle A} , S {\displaystyle S} is a (small) square diagonal matrix with non-negative singular values along the diagonal, and where V {\displaystyleGauss–Newton algorithm (4,204 words) [view diff] exact match in snippet view article find links to article
=-\mathbf {J} ^{\operatorname {T} }\mathbf {r} ,} where D is a positive diagonal matrix. Note that when D is the identity matrix I and λ → + ∞ {\displaystyleParamodular group (878 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\begin{pmatrix}0&F\\-F&0\end{pmatrix}}} where F is an n by n diagonal matrix whose diagonal elements Fii are positive integers with each dividingGreek letters used in mathematics, science, and engineering (3,397 words) [view diff] exact match in snippet view article find links to article
in first-order logic the cosmological constant the lambda baryon a diagonal matrix of eigenvalues in linear algebra a lattice molar conductivity in electrochemistryInvariant convex cone (3,539 words) [view diff] exact match in snippet view article find links to article
g with a unitary transformation, it can be assumed that g(0) is a diagonal matrix with entries λi ≥ 0 with r = λ1 > 0 and that the image of the unitPeter–Weyl theorem (2,480 words) [view diff] exact match in snippet view article find links to article
(\pi (g)).} In the notation above, the character is the sum of the diagonal matrix coefficients: χ π = ∑ i = 1 d ( π ) u i i ( π ) . {\displaystyle \chiLMS color space (3,545 words) [view diff] exact match in snippet view article find links to article
methods, or color appearance models (CAMs), run a von Kries-style diagonal matrix transform in a slightly modified, LMS-like, space instead. They mayDirect sum (2,822 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbf {A} \oplus \mathbf {B} } is defined as the block diagonal matrix of A {\displaystyle \mathbf {A} } and B {\displaystyle \mathbf {B}Projection pursuit regression (1,832 words) [view diff] exact match in snippet view article find links to article
If we solve for all weights w {\displaystyle w} and put them in a diagonal matrix W {\displaystyle W} , stack all the new targets b ^ {\displaystyleSparse dictionary learning (3,496 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \lambda _{i}} are the so-called dual variables forming the diagonal matrix Λ {\displaystyle \Lambda } . We can then provide an analytical expressionExchange interaction (3,400 words) [view diff] exact match in snippet view article find links to article
values of a matrix are its diagonal elements after it is converted to a diagonal matrix. Now, the characteristic values of the square of the magnitude of theGeometrothermodynamics (1,374 words) [view diff] exact match in snippet view article find links to article
1,\ldots ,1)} where ξ a b {\displaystyle \xi _{ab}} is a constant diagonal matrix that can be expressed in terms of δ a b {\displaystyle \delta _{ab}}OPTOS formalism (1,149 words) [view diff] exact match in snippet view article find links to article
redistribution takes occurs on the path, the propagation matrix D is a diagonal matrix. The single entries consist of the Lambert-Beer absorption factor,PageRank (8,783 words) [view diff] exact match in snippet view article find links to article
denotes the adjacency matrix of the graph and K {\displaystyle K} is the diagonal matrix with the outdegrees in the diagonal. The probability calculation isKernel methods for vector output (4,218 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \Sigma \in {\mathcal {\textbf {R}}}^{D\times D}} is a diagonal matrix with elements { σ d 2 } d = 1 D {\displaystyle \left\{\sigmaWhitehead torsion (1,858 words) [view diff] exact match in snippet view article find links to article
matrix can be written as a product of elementary matrices times a diagonal matrix; this follows easily from the fact that Z{\displaystyle \mathbb {Z}Caravelli-Traversa-Di Ventra equation (1,971 words) [view diff] exact match in snippet view article find links to article
memristor; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector X = diag ( X → ) {\displaystyle X=\operatorname {diag}Logarithm of a matrix (2,931 words) [view diff] exact match in snippet view article find links to article
A ′ = V − 1 A V . {\displaystyle A'=V^{-1}AV.\,} Then A′ will be a diagonal matrix whose diagonal elements are eigenvalues of A. Replace each diagonalGaussian network model (4,574 words) [view diff] exact match in snippet view article find links to article
unitary matrix, UT = U−1, of the eigenvectors ui of Γ and Λ is the diagonal matrix of eigenvalues λi. The frequency and shape of a mode is representedPhase retrieval (2,737 words) [view diff] exact match in snippet view article find links to article
Wr{\displaystyle \mathbf {W} _{r}} be the N×N{\displaystyle N\times N} diagonal matrix with diagonal elements (wr[0],wr[1],…,wr[N−1]).{\displaystyle \left(w_{r}[0]Generalized minimal residual method (3,325 words) [view diff] exact match in snippet view article find links to article
squares problem). Note that, for symmetric matrices, a symmetric tri-diagonal matrix is actually achieved, resulting in the MINRES method. Because columnsGraph partition (3,345 words) [view diff] exact match in snippet view article find links to article
{\displaystyle j} , and degree matrix D {\displaystyle D} , which is a diagonal matrix, where each diagonal entry of a row i {\displaystyle i} , d i i {\displaystyleBirefringence (6,582 words) [view diff] exact match in snippet view article find links to article
direction of the optic axis of a uniaxial crystal), resulting in a diagonal matrix for the permittivity tensor ε: where the diagonal values are squaresResonance (7,899 words) [view diff] exact match in snippet view article find links to article
g { k i } {\displaystyle {\bf {K}}={\rm {diag}}\,\{k_{i}\}} is the diagonal matrix of the degrees of the network's nodes. Then, for a network of classicalZonal spherical function (6,693 words) [view diff] exact match in snippet view article find links to article
diagonal matrix with positive entries. Thus g = uaw with w = u* v, so that any K-biinvariant function on G corresponds to a function of the diagonal matrixSchur orthogonality relations (2,618 words) [view diff] exact match in snippet view article find links to article
to the identity representation. The trace of a matrix is a sum of diagonal matrix elements, Tr ( Γ ( R ) ) = ∑ m = 1 l Γ ( R ) m m . {\displaystyleE8 lattice (3,559 words) [view diff] exact match in snippet view article find links to article
The full E8 Weyl group is generated by this subgroup and the block diagonal matrix H4⊕H4 where H4 is the Hadamard matrix H 4 = 1 2 [ 1 1 1 1 1 − 1 1 −Modes of variation (1,668 words) [view diff] exact match in snippet view article find links to article
\mathbf {\Sigma } } , and Λ {\displaystyle \mathbf {\Lambda } } is a diagonal matrix whose entries are the eigenvalues of Σ {\displaystyle \mathbf {\SigmaMinimum mean square error (9,310 words) [view diff] exact match in snippet view article find links to article
observation noise is uncorrelated. That is, C Z {\displaystyle C_{Z}} is a diagonal matrix. In such cases, it is advantageous to consider the components of yPropagation of uncertainty (3,982 words) [view diff] exact match in snippet view article find links to article
words, even if Σ x {\displaystyle {\boldsymbol {\Sigma }}^{x}} is a diagonal matrix, Σ f {\displaystyle {\boldsymbol {\Sigma }}^{f}} is in general a fullClosed-subgroup theorem (2,891 words) [view diff] exact match in snippet view article find links to article
generated by X is not closed if and only if X is similar over C to a diagonal matrix with two entries of irrational ratio. Let h ⊂ g be a Lie subalgebraClosed-subgroup theorem (2,891 words) [view diff] exact match in snippet view article find links to article
generated by X is not closed if and only if X is similar over C to a diagonal matrix with two entries of irrational ratio. Let h ⊂ g be a Lie subalgebraSimplex (7,842 words) [view diff] exact match in snippet view article find links to article
orthogonal matrix Q, there is a choice of basis in which Q is a block diagonal matrix Q = diag ( Q 1 , Q 2 , … , Q k ) , {\displaystyle Q=\operatornameKnowledge graph embedding (5,914 words) [view diff] exact match in snippet view article find links to article
relation is a diagonal matrix, the scoring function can not distinguish asymmetric facts. ComplEx: As DistMult uses a diagonal matrix to represent theTesting in binary response index models (998 words) [view diff] exact match in snippet view article find links to article
{V}}D^{T}/n)^{-1}(D{\hat {\beta }}_{u}){\xrightarrow {d}}X_{Q}^{2}} Where D is a diagonal matrix with the last Q diagonal entries as 0 and others as 1. If the restrictedChern–Weil homomorphism (2,779 words) [view diff] exact match in snippet view article find links to article
so that, in the matrix term, Ω {\displaystyle \Omega } is the block diagonal matrix with ΩI's on the diagonal. Then, since det ( I − t Ω 2 π i ) = detDegenerate energy levels (6,123 words) [view diff] exact match in snippet view article find links to article
eigenbasis of A ^ {\displaystyle {\hat {A}}} is not a diagonal but a block diagonal matrix, i.e. the degenerate eigenvectors of A ^ {\displaystyle {\hat {A}}}Restricted representation (3,061 words) [view diff] exact match in snippet view article find links to article
are complex numbers. Each matrix U in Sp(N) is conjugate to a block diagonal matrix with entries q i = ( z i 0 0 z ¯ i ) , {\displaystyleMatrix differential equation (2,514 words) [view diff] exact match in snippet view article find links to article
diagonalisation and leveraging the property that the matrix exponential of a diagonal matrix is the same as element-wise exponentiation of its elements)Substitution model (8,833 words) [view diff] exact match in snippet view article find links to article
&\ddots &\vdots \\0&\ldots &\lambda _{4}\end{pmatrix}}\,,} where Λ is a diagonal matrix and where { λ i } {\displaystyle \lbrace \lambda _{i}\rbrace } areQuantum entanglement (12,919 words) [view diff] exact match in snippet view article find links to article
entangled state if the reduced state of each subsystem of ρ is the diagonal matrix [ 1 n ⋱ 1 n ] . {\displaystyle {\begin{bmatrix}{\frac {1}{n}}&&\\&\ddotsPermanent (mathematics) (4,508 words) [view diff] exact match in snippet view article
{1}{\det(I-XA)}},} where I is the order n identity matrix and X is the diagonal matrix with diagonal [ x 1 , x 2 , … , x n ] . {\displaystyle [x_{1},x_{2}Viscous stress tensor (2,460 words) [view diff] exact match in snippet view article find links to article
in question. (It is represented in any coordinate system by a 3 × 3 diagonal matrix with equal values along the diagonal.) It is numerically equal to 1/3Gaussian process approximations (1,982 words) [view diff] exact match in snippet view article find links to article
}}=K\left({\bar {X}},{\bar {X}}\right)} and D{\displaystyle \mathbf {D} } is a diagonal matrix. Depending on the method and application various ways of selectingBlack hole information paradox (8,333 words) [view diff] exact match in snippet view article find links to article
}}\!(r)]\}\end{aligned}}} The first term of H {\displaystyle H} is a diagonal matrix representing the microscopic state of black holes no heavier than theHolomorphic functional calculus (5,479 words) [view diff] exact match in snippet view article find links to article
disc containing only λi from the spectrum. The corresponding block-diagonal matrix ⨁ i T i {\displaystyle \bigoplus _{i}T_{i}} is the Jordan canonicalChristoffel symbols (7,076 words) [view diff] exact match in snippet view article find links to article
\eta _{ab}=\delta _{ab}} . For pseudo-Riemannian manifolds, it is the diagonal matrix having signature ( p , q ) {\displaystyle (p,q)} . The notation e iHadamard's maximal determinant problem (2,385 words) [view diff] exact match in snippet view article find links to article
can be written as B−J where J is the all-one matrix and B is a block-diagonal matrix whose diagonal blocks are of the form (n-3)I+4J. Moreover, he showedEight-point algorithm (2,799 words) [view diff] exact match in snippet view article find links to article
{V} } are orthogonal matrices and S{\displaystyle \mathbf {S} } is a diagonal matrix which contains the singular values of Eest{\displaystyle \mathbf {E}Diffusion MRI (9,171 words) [view diff] exact match in snippet view article find links to article
_{1}+\lambda _{2}+\lambda _{3}} where Λ {\displaystyle \Lambda } is a diagonal matrix with eigenvalues λ 1 {\displaystyle \lambda _{1}} , λ 2 {\displaystyleSpin representation (4,460 words) [view diff] exact match in snippet view article find links to article
abelian subalgebra. Let ε1, ... εm be the basis of h∗ such that, for a diagonal matrix A, εk(ρA) is the kth diagonal entry of A. Clearly this is a basis forEssential matrix (3,215 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbf {\Sigma } } is a 3 × 3 {\displaystyle 3\times 3} diagonal matrix with Σ = ( s 0 0 0 s 0 0 0 0 ) {\displaystyle \mathbf {\Sigma }Generalized additive model (5,683 words) [view diff] exact match in snippet view article find links to article
coefficients' freedom to vary. For example, if W {\displaystyle W} is the diagonal matrix of IRLS weights at convergence, and X {\displaystyle X} is the GAMRate equation (7,441 words) [view diff] exact match in snippet view article find links to article
\operatorname {diag} } be the function that takes a vector and constructs a diagonal matrix whose on-diagonal entries are those of the vector. Let L − 1 {\displaystyleVector generalized linear model (4,737 words) [view diff] exact match in snippet view article find links to article
package has an xij argument that allows the successive elements of the diagonal matrix to be inputted. Yee (2015) describes an R package implementation inMethod of steepest descent (5,057 words) [view diff] exact match in snippet view article find links to article
1 {\displaystyle S''_{zz}(0)=PJ_{z}P^{-1}} , where Jz is an upper diagonal matrix containing the eigenvalues and det P ≠ 0; hence, det S z z ″ ( 0 )Affine term structure model (2,599 words) [view diff] exact match in snippet view article find links to article
={\begin{pmatrix}1&1&0\end{pmatrix}}^{T}} and Ω {\displaystyle \Omega } is a diagonal matrix with entries Ω i i = σ i 2 {\displaystyle \Omega _{ii}=\sigma _{i}^{2}}Lorentz group (9,740 words) [view diff] exact match in snippet view article find links to article
{for} \,\mathrm {all} \,t\right\}} . If η {\displaystyle \eta } is the diagonal matrix with diagonal entries (1, −1, −1, −1), then the Lie algebra o ( 1Foldy–Wouthuysen transformation (3,133 words) [view diff] exact match in snippet view article find links to article
representation (after Paul Dirac and Wolfgang Pauli) in which it is a diagonal matrix): By elementary trigonometry, 6 also implies that: so that using 8Matroid parity problem (2,829 words) [view diff] exact match in snippet view article find links to article
{\begin{pmatrix}0&M\\M^{T}&T\end{pmatrix}}-m,} where T{\displaystyle T} is a block diagonal matrix whose blocks are 2×2{\displaystyle 2\times 2} submatrices of the formGraphon (5,459 words) [view diff] exact match in snippet view article find links to article
matrix of ( K n , n ) {\displaystyle (K_{n,n})} looks like a block off-diagonal matrix, with two blocks of ones and two blocks of zeros. For example, theMemristor (13,866 words) [view diff] exact match in snippet view article find links to article
\Omega X)^{-1}\Omega {\vec {S}}} where X {\displaystyle X} is the diagonal matrix with elements x i {\displaystyle x_{i}} on the diagonal, α , β , χSpace-time adaptive processing (2,807 words) [view diff] exact match in snippet view article find links to article
techniques or diagonal-loading SMI (where a small magnitude, random diagonal matrix is added to attempt to stabilize the matrix prior to inverting). ThisCauchy stress tensor (8,309 words) [view diff] exact match in snippet view article find links to article
are the principal stresses and the stress tensor is represented by a diagonal matrix: σ i j = [ σ 1 0 0 0 σ 2 0 0 0 σ 3 ] {\displaystyle \sigmaSymmetric cone (16,607 words) [view diff] exact match in snippet view article find links to article
Hr(A) there is an algebra automorphism carrying the matrix onto a diagonal matrix with real entries; it is then straightforward to check that [L(a),L(b)]Symmetric cone (16,607 words) [view diff] exact match in snippet view article find links to article
Hr(A) there is an algebra automorphism carrying the matrix onto a diagonal matrix with real entries; it is then straightforward to check that [L(a),L(b)]Multivariate kernel density estimation (4,225 words) [view diff] exact match in snippet view article find links to article
classes. Left. S positive scalar times the identity matrix. Centre. D diagonal matrix with positive entries on the main diagonal. Right. F symmetric positiveKalman filter (20,328 words) [view diff] exact match in snippet view article find links to article
where U is a unit triangular matrix (with unit diagonal), and D is a diagonal matrix. Between the two, the U-D factorization uses the same amount of storageStrong subadditivity of quantum entropy (4,679 words) [view diff] exact match in snippet view article find links to article
_{12}} (and similarly, σ 12 {\displaystyle \sigma _{12}} ) to be block diagonal matrix with blocks λ k ρ k {\displaystyle \lambda _{k}\rho _{k}} (and λ kClassical XY model (4,832 words) [view diff] exact match in snippet view article find links to article
_{n}\psi _{n}^{*}(\theta ')\psi _{n}(\theta )} which represents a diagonal matrix representation in the basis of its plane-wave eigenfunctions ψ = expHayes-Wheelwright matrix (2,452 words) [view diff] exact match in snippet view article find links to article
to take advantage of economies of scale. Firms operating along the diagonal matrix are assumed to perform better than those too far from the diagonalTwo-state quantum system (6,568 words) [view diff] exact match in snippet view article find links to article
boundary conditions on how it acts on a general state.) This results in a diagonal matrix with the diagonal elements being the energies of the eigenstates andManifold regularization (3,649 words) [view diff] exact match in snippet view article find links to article
x_{i}} and xj{\displaystyle x_{j}}. Define D{\displaystyle D} to be a diagonal matrix with Dii=∑j=1ℓ+uWij{\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}}Eigenmoments (3,096 words) [view diff] exact match in snippet view article find links to article
{\displaystyle P^{T}BP=D_{B}} . Where D B {\displaystyle D_{B}} is a diagonal matrix sorted in increasing order. Since B {\displaystyle B} is positive definiteSpillover (experiment) (2,490 words) [view diff] exact match in snippet view article
exposure probabilities for each unit in the analysis. First, define a diagonal matrix with a vector of treatment assignment probabilities P=diag(pz1,pz23D rotation group (11,400 words) [view diff] exact match in snippet view article find links to article
axis fixed (Euler's rotation theorem), and is conjugate to a block diagonal matrix of the form D = ( cos θ − sin θ 0 sin θ cos θ 0 0 0 1 ) = eOscillator representation (21,529 words) [view diff] exact match in snippet view article find links to article
latter is obtained by taking the transpose and conjugating by the diagonal matrix with entries ±1. Hence H also contains ( a ¯ − c ¯ − b ¯ d ¯ ) . {\displaystyleGeneralized singular value decomposition (4,126 words) [view diff] exact match in snippet view article find links to article
^{+}=\left\lceil E_{1}^{+},E_{2}^{+}\right\rfloor } for any block-diagonal matrix. Then define A i + = Q [ Y − 1 0 ] Σ i + U i ∗ {\displaystyleCMA-ES (7,543 words) [view diff] exact match in snippet view article find links to article
of C {\displaystyle C} remark first that this is the case for any diagonal matrix C {\displaystyle C} , because the coordinate-wise maximizer is independentHook length formula (5,141 words) [view diff] exact match in snippet view article find links to article
_{k}(\mathbb {C} )} , and the Schur polynomial is also the character of the diagonal matrix d i a g ( x 1 , … , x k ) {\displaystyle \mathrm {diag} (x_{1},\ldotsBiological motion perception (4,058 words) [view diff] exact match in snippet view article find links to article
radial basis function for each neuron and C{\displaystyle C} is a diagonal matrix which contains elements that have been set during training and correspondKhatri–Rao product (4,210 words) [view diff] exact match in snippet view article find links to article
and in optimizing the solution of inverse problems dealing with a diagonal matrix. In 1996 the column-wise Khatri–Rao product was proposed to estimateCapelli's identity (6,217 words) [view diff] exact match in snippet view article find links to article
matrix with elements Qil, and diag(n − 1, n − 2, ..., 1, 0) means the diagonal matrix with the elements n − 1, n − 2, ..., 1, 0 on the diagonal. See propositionCharlieplexing (9,006 words) [view diff] exact match in snippet view article find links to article
failure characteristics of the device being designed. LED failure in a diagonal matrix: Due to the fact that the layout of a standard vertical/horizontalHermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article
the case of H = SU(2) the symmetry σ is given by conjugation by the diagonal matrix with entries ±i so that σ ( α β − β ¯ α ¯ ) = ( α − β β ¯ α ¯ ) {\displaystyleErgodic flow (5,093 words) [view diff] exact match in snippet view article find links to article
spectral subspace corresponding to the interval [a,b]. Let g(s) be the diagonal matrix with entries s and s−1 for |s| > 1. Then g(s)P[a,b]g(s)−1 = P[s2a,Biochemical systems equation (2,318 words) [view diff] exact match in snippet view article find links to article
Since each parameter only affects one reaction, the matrix will be a diagonal matrix: E = [ ∂ v 1 ∂ k 1 0 0 0 0 ∂ v 2 ∂ k 2 0 0 0 0 ∂ v 3 ∂ k 3 0 0 0 ∂Light-front quantization applications (9,006 words) [view diff] exact match in snippet view article find links to article
the basis, corresponding to fixed number of particles, it is a non-diagonal matrix. Its eigenvector—the state vector of a physical system—is an infiniteInfinitesimal rotation matrix (2,787 words) [view diff] exact match in snippet view article find links to article
R=QSQ^{\textsf {T}},} where Q {\displaystyle Q} is orthogonal and S is a block diagonal matrix with ⌊ n / 2 ⌋ {\textstyle \lfloor n/2\rfloor } blocks of order 2,Model-based clustering (3,478 words) [view diff] exact match in snippet view article find links to article
g}{\displaystyle A_{g}={\mbox{diag}}\{A_{1,g},\ldots ,A_{d,g}\}} is a diagonal matrix whose elements are proportional to the eigenvalues of Σg{\displaystyleHamiltonian cycle polynomial (2,247 words) [view diff] exact match in snippet view article find links to article
doesn't depend on the matrix's diagonal entries, adding an arbitrary diagonal matrix doesn't change this polynomial too. These two types of transformationMutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article
corresponds to the automorphism of E = Hp + q(R) given by conjugating by the diagonal matrix with p diagonal entries equal to 1 and q to −1. Without loss of generalityDifferential forms on a Riemann surface (10,756 words) [view diff] exact match in snippet view article find links to article
+ |λ|2)−(k−j)/2. It is therefore compact because it is given by a diagonal matrix with diagonal entries tending to zero. Elliptic regularity (Weyl'sWaste input-output model (3,181 words) [view diff] exact match in snippet view article find links to article
{x}}_{T}^{-1}.\end{aligned}}} Here, v ^ {\displaystyle {\hat {v}}} refers to a diagonal matrix where the ( i , i ) {\displaystyle (i,i)} element is the i {\displaystyleForce control (3,692 words) [view diff] exact match in snippet view article find links to article
matrix Σ indicates which space directions are restricted and is a diagonal matrix consisting of zeros and ones. Which spatial direction is restrictedFinite subgroups of SU(2) (3,911 words) [view diff] exact match in snippet view article
representing g in Vj is just S2j ( g ). Since every g is conjugate to a diagonal matrix with diagonal entries ζ{\displaystyle \zeta } and ζ−1{\displaystyleLight-front computational methods (11,024 words) [view diff] exact match in snippet view article find links to article
left eigenstates. This construction can be extended to include off-diagonal matrix elements and gauge projections. Physical quantities can then be computed