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Longer titles found: Semi-orthogonal matrix (view)

searching for Orthogonal matrix 27 found (149 total)

Procrustes analysis (1,822 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 (1,138 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

Independent component analysis (7,503 words) [view diff] exact match in snippet view article find links to article

estimating a general matrix A {\displaystyle A} to estimating an orthogonal matrix V {\displaystyle V} , significantly simplifying the search for independent

Kernel-independent component analysis (516 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

Alice Guionnet (1,070 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

Student's t-test (7,011 words) [view diff] exact match in snippet view article find links to article

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

Automorphism of a Lie algebra (715 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 ( 2 n ) {\displaystyle O(2n)} with determinant −1. A derivation

Inverse-Wishart distribution (3,482 words) [view diff] exact match in snippet view article find links to article

{I} } , and Φ {\displaystyle {\mathcal {\Phi }}} is an arbitrary orthogonal matrix, replacement of X {\displaystyle \mathbf {X} } by Φ X Φ T {\displaystyle

Rotation (4,090 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

Quadratic form (4,569 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

Random projection (1,829 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 (4,489 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) ( X 4 Y 4 Z 4 ) = ( cos ⁡ δ 0 − sin ⁡ δ 0

Conway group (2,300 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

Graeme Gunn (2,082 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

Chi-squared distribution (6,817 words) [view diff] exact match in snippet view article find links to article

( b 1 , . . . , b n ) {\displaystyle Q:=(b_{1},...,b_{n})} is an orthogonal matrix. Since also X := Q ⊤ Z ∼ N ( 0 ¯ , Q ⊤ 1 1 Q ) = N ( 0 ¯ , 1 1 ) {\displaystyle

Restricted representation (3,061 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 (7,418 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 (7,036 words) [view diff] exact match in snippet view article find links to article

μ ( x ) {\displaystyle R_{\nu }^{\mu }(x)} is a rotation (i.e. an orthogonal matrix) or Lorentz transformation. The conformal group of Euclidean space

Screw theory (4,410 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

Cholesky decomposition (8,335 words) [view diff] exact match in snippet view article find links to article

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

Conjugate gradient method (8,446 words) [view diff] exact match in snippet view article find links to article

T {\displaystyle A=QDQ^{T}} where Q {\displaystyle Q} is a random orthogonal matrix and D {\displaystyle D} is a diagonal matrix with eigenvalues ranging

Uniform distribution on a Stiefel manifold (1,170 words) [view diff] exact match in snippet view article find links to article

n ) {\displaystyle X=(x_{1},\dots ,x_{n})} . We extend this to an orthogonal matrix [ X : X ⊥ ] = ( x 1 , … , x p ) ∈ O ( p ) {\displaystyle [X:X^{\perp

Random feature (1,705 words) [view diff] exact match in snippet view article find links to article

distance between datapoints. Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. In NIPS 2006, deep learning had

List of numerical analysis topics (8,335 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) (7,750 words) [view diff] exact match in snippet view article

Clebsch–Gordan coefficients. The Clebsch–Gordan coefficients form a real orthogonal matrix. Therefore, ϕ μ 1 ν 1 ϕ μ 2 ν 2 = ∑ μ , ν , γ ( μ 1 μ 2 γ ν 1 ν 2

Angular velocity tensor (2,523 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 A T {\displaystyle A^{\mathsf

Lagrangian coherent structure (10,382 words) [view diff] exact match in snippet view article find links to article

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