In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed...

In mathematics, in particular functional analysis, the singular values of a compact operator T : X → Y {\displaystyle T:X\rightarrow Y} acting between...

algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD). The...

In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for...

extends naturally to perturbation of singular values. This result gives the bound for the perturbation in the singular values of a matrix M {\displaystyle M}...

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...

Quantum singular value transformation is a framework for designing quantum algorithms. It encompasses a variety of quantum algorithms for problems which...

efficient computations. Hermitian matrices also appear in techniques like singular value decomposition (SVD) and eigenvalue decomposition. In statistics and...

In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded...

often computed by eigendecomposition of the data covariance matrix or singular value decomposition of the data matrix. PCA is the simplest of the true eigenvector-based...