 Singular value decomposition

Every complex matrix has a factorization $A=V\Sigma U^{†}$ with $U,V$ unitary and $\Sigma$ diagonal with nonnegative entries. The squared singular values are the eigenvalues of $A^{†}A$.

Singular Value Decomposition (SVD) is a mathematical technique in linear algebra used to factorize a matrix into three other matrices. It is particularly useful for analyzing and reducing the dimensionality of data, solving linear equations, and performing principal component analysis.