the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD). The two versions... 22 KB (4,126 words) - 06:55, 17 December 2023 |
multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type... 26 KB (4,129 words) - 22:32, 9 April 2024 |
Spectral theorem (redirect from Eigen-value decomposition) of normal matrices below). The spectral decomposition is a special case of the singular value decomposition, which states that any matrix A ∈ C m × n... 24 KB (3,618 words) - 14:59, 26 April 2024 |
the singular value decomposition. Hence, the existence of the polar decomposition is equivalent to the existence of the singular value decomposition. Applicable... 26 KB (3,580 words) - 17:05, 12 March 2024 |
Principal component analysis (category Matrix decompositions) multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (invented in the last quarter... 113 KB (14,214 words) - 16:04, 24 April 2024 |
behind the construction of the polar decomposition is similar to that used to compute the singular-value decomposition. If A {\displaystyle A} is normal... 24 KB (4,173 words) - 01:35, 12 April 2024 |
between the singular value decomposition and eigenvalue decompositions. This means that most methods for computing the singular value decomposition are similar... 18 KB (2,507 words) - 03:52, 21 December 2023 |
Moore–Penrose inverse (category Singular value decomposition) entries are real or complex numbers. It can be computed using the singular value decomposition. In the special case where A {\displaystyle A} is a normal matrix... 46 KB (7,421 words) - 02:36, 21 April 2024 |
the singular-value decomposition. Given the singular value decomposition A = U Σ V T {\displaystyle A=U\Sigma V^{\mathsf {T}}} with singular values σ i... 30 KB (3,902 words) - 03:51, 25 March 2024 |
In linear algebra, two-dimensional singular-value decomposition (2DSVD) computes the low-rank approximation of a set of matrices such as 2D images or weather... 3 KB (518 words) - 19:10, 28 September 2023 |
from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the... 57 KB (7,603 words) - 04:20, 11 April 2024 |
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of... 28 KB (4,633 words) - 17:41, 29 March 2024 |
variation of the CP decomposition. Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal... 36 KB (6,259 words) - 02:26, 9 March 2024 |
Non-linear least squares (category CS1: long volume value) triangular. A variant of the method of orthogonal decomposition involves singular value decomposition, in which R is diagonalized by further orthogonal... 28 KB (4,538 words) - 09:54, 25 April 2024 |
unique up to re-ordering. The Schmidt decomposition is essentially a restatement of the singular value decomposition in a different context. Fix orthonormal... 8 KB (1,210 words) - 23:28, 20 June 2023 |
and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s... 9 KB (1,435 words) - 11:48, 18 June 2023 |
(LU decomposition) can be unreliable, and a rank-revealing decomposition should be used instead. An effective alternative is the singular value decomposition... 29 KB (4,390 words) - 09:07, 22 March 2024 |
right-triangular system Rx=QTb.{\displaystyle Rx=Q^{T}b.} The Singular Value Decomposition (SVD) of a (tall) matrix A{\displaystyle A} is the representation... 15 KB (2,152 words) - 11:15, 3 March 2024 |
Hermitian matrix (section Singular values) Hermitian matrices also appear in techniques like singular value decomposition (SVD) and eigenvalue decomposition. In statistics and machine learning, Hermitian... 19 KB (2,985 words) - 20:42, 29 March 2024 |
} Applying singular-value decomposition (SVD) to matrix A{\displaystyle A} with dimensions p×m{\displaystyle p\times m} produces a singular system consisting... 15 KB (2,695 words) - 16:20, 30 November 2023 |
fields. The main tensor decompositions are: Tensor rank decomposition; Higher-order singular value decomposition; Tucker decomposition; matrix product states... 7 KB (752 words) - 20:41, 9 April 2024 |
algebra, the complete orthogonal decomposition is a matrix decomposition. It is similar to the singular value decomposition, but typically somewhat cheaper... 6 KB (748 words) - 21:18, 11 December 2023 |
{D}}{\big )}\leq r} has an analytic solution in terms of the singular value decomposition of the data matrix. The result is referred to as the matrix approximation... 22 KB (3,596 words) - 04:11, 15 April 2024 |
Orthogonal matrix (section Decompositions) triangular Singular value decomposition M = UΣVT, U and V orthogonal, Σ diagonal matrix Eigendecomposition of a symmetric matrix (decomposition according... 36 KB (4,802 words) - 22:52, 2 February 2024 |
RRQR factorization (category Matrix decompositions) matrix decomposition algorithm based on the QR factorization which can be used to determine the rank of a matrix. The singular value decomposition can be... 2 KB (138 words) - 14:47, 30 March 2024 |
left and right singular vectors of the original matrix M{\displaystyle M} representing an approximate Truncated singular value decomposition (SVD) with left... 15 KB (2,511 words) - 09:03, 18 December 2023 |
Rank factorization (category Matrix decompositions) construct a full-rank factorization of A{\textstyle A} via a singular value decomposition A=UΣV∗=[U1U2][Σr000][V1∗V2∗]=U1(ΣrV1∗).{\displaystyle A=U\Sigma... 12 KB (1,721 words) - 18:49, 16 October 2022 |