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Longer titles found: Semi-orthogonal matrix (view)

searching for Orthogonal matrix 23 found (143 total)

Procrustes analysis (1,762 words) [view diff] exact match in snippet view article find links to article

orthogonal Procrustes problem, subject to det(R) = 1 (where R is an orthogonal matrix), is a method which can be used to determine the optimal rotation

Free convolution (1,126 words) [view diff] no match in snippet view article find links to article

them is invariant, in law, under conjugation by any unitary (resp. orthogonal) matrix and such that the empirical spectral measures of A{\displaystyle A}

Kernel-independent component analysis (502 words) [view diff] exact match in snippet view article find links to article

Kernel ICA estimates a m×m{\displaystyle m\times m} dimensional orthogonal matrix A{\displaystyle \mathbf {A} } so as to minimize finite-sample F{\displaystyle

Student's t-test (6,435 words) [view diff] exact match in snippet view article find links to article

(PT)n×n{\displaystyle (P^{T})_{n\times n}} be an n×n{\displaystyle n\times n} orthogonal matrix whose elements of the first row are all 1/n{\displaystyle 1/{\sqrt

Alice Guionnet (1,066 words) [view diff] exact match in snippet view article find links to article

Guionnet & E. Maurel Segala (2009). "Asymptotics of unitary and orthogonal matrix integrals". Advances in Mathematics. 222: 172–215. arXiv:math/0608193

Automorphism of a Lie algebra (695 words) [view diff] exact match in snippet view article find links to article

D_{n}={\mathfrak {so}}(2n)}, the automorphism is obtained by conjugating by an orthogonal matrix in O(2n){\displaystyle O(2n)} with determinant -1. A derivation on

Inverse-Wishart distribution (3,181 words) [view diff] exact match in snippet view article find links to article

}}=\mathbf {I} ,{\text{ and }}{\mathcal {\Phi }}} is an arbitrary orthogonal matrix, replacement of X{\displaystyle \mathbf {X} } by ΦXΦT{\displaystyle

Rotation (3,840 words) [view diff] exact match in snippet view article find links to article

stretching it. If we write A in this basis, it is diagonal; but a diagonal orthogonal matrix is made of just +1s and −1s in the diagonal entries. Therefore, we

Random projection (1,487 words) [view diff] exact match in snippet view article find links to article

the following properties are satisfied: Spherical symmetry: For any orthogonal matrix A∈O(d){\displaystyle A\in O(d)}, RA and R have the same distribution

Gyrocompass (3,896 words) [view diff] exact match in snippet view article find links to article

Z_{4}}-axis) of the barycenter. This can be achieved by the following orthogonal matrix (with unit determinant) (X4Y4Z4)=(cos⁡δ0−sin⁡δ010sin⁡δ0cos⁡δ)(X3Y3Z3)

Quadratic form (4,379 words) [view diff] exact match in snippet view article find links to article

&0\\0&0&\cdots &\lambda _{n}\end{pmatrix}}} by a suitable choice of an orthogonal matrix S, and the diagonal entries of B are uniquely determined – this is

Chi-squared distribution (6,005 words) [view diff] exact match in snippet view article find links to article

so that Q:=(b1,...,bn){\displaystyle Q:=(b_{1},...,b_{n})} is an orthogonal matrix. Since also X:=Q⊤Z∼N(0¯,Q⊤11Q)=N(0¯,11){\displaystyle X:=Q^{\top }\

Conway group (2,270 words) [view diff] exact match in snippet view article find links to article

of 6 matrices: odd numbers each of η and −η. ζ is a symmetric and orthogonal matrix, thus an involution. Some experimenting shows that it interchanges

Restricted representation (2,907 words) [view diff] exact match in snippet view article find links to article

representations and in ½ + Z for spin representations. In fact if an orthogonal matrix U has eigenvalues zi±1 for 1 ≤ i ≤ n, then the character of the corresponding

Hermitian symmetric space (7,298 words) [view diff] exact match in snippet view article find links to article

symmetric matrices they can be simultaneously diagonalized by a real orthogonal matrix W. So UMUt is diagonal if U = WVt. Type IIn: for every complex skew

Conformal field theory (6,361 words) [view diff] exact match in snippet view article find links to article

and Rνμ(x){\displaystyle R_{\nu }^{\mu }(x)} is a rotation (i.e. an orthogonal matrix) or Lorentz transformation. The conformal group is locally isomorphic

Screw theory (4,212 words) [view diff] exact match in snippet view article find links to article

dual matrix [Â] = ([A], [DA]) has determinant 1 and is called a dual orthogonal matrix. Consider the movement of a rigid body defined by the parameterized

Graeme Gunn (1,918 words) [view diff] exact match in snippet view article find links to article

character. Construction Date: 1968 The design is based on a 2700 orthogonal matrix using natural tree trunks, some 10 metres long farmed from a local

Cholesky decomposition (6,855 words) [view diff] exact match in snippet view article find links to article

V=UΣ−1/2{\displaystyle V=U\Sigma ^{-1/2}} where U{\displaystyle U} is an orthogonal matrix. This then yields A=UΣUT{\displaystyle A=U\Sigma U^{T}}. The Cholesky

List of numerical analysis topics (8,342 words) [view diff] exact match in snippet view article find links to article

decomposition — lower triangular times upper triangular QR decomposition — orthogonal matrix times triangular matrix RRQR factorization — rank-revealing QR factorization

Clebsch–Gordan coefficients for SU(3) (6,878 words) [view diff] exact match in snippet view article

Clebsch–Gordan coefficients. The Clebsch–Gordan coefficients form a real orthogonal matrix. Therefore, ϕμ1ν1ϕμ2ν2=∑μ,ν,γ(μ1μ2γν1ν2ν)ψ(μ1μ2γν).{\displaystyle

Angular velocity tensor (2,309 words) [view diff] exact match in snippet view article find links to article

{dA}{dt}}A^{-1}={\frac {dA}{dt}}A^{\mathsf {T}},} since the inverse of an orthogonal matrix A{\displaystyle A} is its transpose AT{\displaystyle A^{\mathsf {T}}}

Lagrangian coherent structure (9,313 words) [view diff] exact match in snippet view article find links to article

Q(t){\displaystyle Q(t)} is an arbitrary 3×3{\displaystyle 3\times 3} proper orthogonal matrix representing time-dependent rotations; and b(t){\displaystyle b(t)}