In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.
It is the generalization of the eigendecomposition of a positive semidefinite normal matrix (for example, a symmetric matrix with positive eigenvalues) to any matrix via an extension of the polar decomposition. It has many useful applications in signal processing and statistics.
Formally, the singular value decomposition of an complex matrix is a factorization of the form , where is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, and is an complex unitary matrix. The diagonal entries of are known as the singular values of . The columns of and the columns of are called the left-singular vectors and right-singular vectors of , respectively.
The singular-value decomposition can be computed using the following observations:
This article uses material from the Wikipedia Simple English article Singular value decomposition, which is released under the Creative Commons Attribution-ShareAlike 3.0 license ("CC BY-SA 3.0"); additional terms may apply (view authors). Content is available under CC BY-SA 4.0 unless otherwise noted. Images, videos and audio are available under their respective licenses.
®Wikipedia is a registered trademark of the Wiki Foundation, Inc. Wiki Simple English (DUHOCTRUNGQUOC.VN) is an independent company and has no affiliation with Wiki Foundation.