Singular value decomposition is a type of factorization that decomposes a matrix into a product of three matrices. The singular value decomposition is a generalization of the previously discussed eigenvalue decomposition. The svd function in the numpy.linalg package can perform this decomposition. This function returns three matrices – U, Sigma, and V – such that U and V are orthogonal and Sigma contains the singular values of the input matrix.

The asterisk denotes the Hermitian conjugate or the conjugate transpose.