Overview - 2023.2 English

Vitis Libraries

Release Date
2023-12-20
Version
2023.2 English

SVD is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \(m\times n\) matrix. It is related to the polar decomposition.

the singular value decomposition of a :math: mtimes n complex matrix \(M\) is a factorization of the form \(U\)\(\Sigma\)\(V^*\), where \(U\) is a \(m\times m\) complex unitary matrix, \(\Sigma\) is a \(m\times n\) rectangular diagonal matrix with non-negative real numbers on the diagonal, and \(V\) is a \(n\times n\) complex unitary matrix. If \(M\) is real, \(U\) and \(V\) can also be guaranteed to be real orthogonal matrix.

\[M = U{\Sigma}V^*\]

The diagonal entries \(\Sigma_{ii}\) of \(\Sigma\) are known as the singular values of \(M\). The number of non-zero singular values is equal to the rank of \(M\). the Columns of \(U\) and \(V\) are called the left-singular vectors and right-singular vectors of \(M\) respectively.