In linear algebra, the singular value decomposition (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 mxn matrix.It is related to the polar decomposition.
Specifically, the singular value decomposition of an mxn complex matrix M is a factorization of the form M= U sigma Vh, where U is m x m unitay matrix, sigma is is an mxn rectangular diagonal matrix with non-negative real numbers on the diagonal, V is a nxn unitary matrix ,transpose of which is vh
Mathematical applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix..