m\times n} matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex...
86 KB (13,745 words) - 15:27, 19 September 2024
rectangular diagonal matrix with the singular values lying on the diagonal. This is the singular value decomposition. For A ∈ C m × n {\displaystyle A\in...
9 KB (1,651 words) - 17:16, 5 September 2024
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...
27 KB (4,239 words) - 03:38, 8 August 2024
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
Spectral theorem (redirect from Eigen-value decomposition)
Matrix decomposition Canonical form Jordan decomposition, of which the spectral decomposition is a special case. Singular value decomposition, a generalisation...
25 KB (3,630 words) - 02:59, 18 May 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...
114 KB (14,310 words) - 10:18, 20 September 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 (3,905 words) - 11:41, 24 August 2024
Moore–Penrose inverse (category Singular value decomposition)
pseudoinverse is by using the singular value decomposition. If A = U Σ V ∗ {\displaystyle A=U\Sigma V^{*}} is the singular value decomposition of A {\displaystyle...
46 KB (7,504 words) - 07:26, 31 August 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...
25 KB (4,220 words) - 03:42, 18 May 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 (6,308 words) - 12:13, 16 May 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
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 (1,331 words) - 19:21, 29 May 2024
interpretation. The name "singular spectrum analysis" relates to the spectrum of eigenvalues in a singular value decomposition of a covariance matrix, and...
42 KB (6,725 words) - 04:51, 27 May 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) - 20:42, 17 September 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 (4,632 words) - 13:25, 12 September 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
and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s...
9 KB (1,499 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) - 03:18, 12 September 2024
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...
58 KB (7,627 words) - 10:10, 25 August 2024
right-triangular system R x = Q T b . {\displaystyle Rx=Q^{T}b.} The Singular Value Decomposition (SVD) of a (tall) matrix A {\displaystyle A} is the representation...
15 KB (2,204 words) - 00:12, 22 July 2024
algebra, the complete orthogonal decomposition is a matrix decomposition. It is similar to the singular value decomposition, but typically somewhat cheaper...
6 KB (774 words) - 21:18, 11 December 2023
fields. The main tensor decompositions are: Tensor rank decomposition; Higher-order singular value decomposition; Tucker decomposition; matrix product states...
7 KB (755 words) - 20:41, 9 April 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...
20 KB (3,013 words) - 18:34, 4 August 2024
diagonal matrix whose diagonal values are in general complex. The left and right singular vectors in the singular value decomposition of a normal matrix A = U...
13 KB (1,656 words) - 01:07, 5 June 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 (2,863 words) - 16:20, 30 November 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 (3,855 words) - 22:28, 7 August 2024
Rank factorization (category Matrix decompositions)
construct a full-rank factorization of A {\textstyle A} via a singular value decomposition A = U Σ V ∗ = [ U 1 U 2 ] [ Σ r 0 0 0 ] [ V 1 ∗ V 2 ∗ ] = U 1...
12 KB (1,943 words) - 18:49, 16 October 2022
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) - 16:45, 22 May 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