On constructing matrices with prescribed singular values and diagonal elements Original Research Article

Similar to the well known Schur-Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix, the Sing-Thompson theorem characterizes the relationship between the diagonal entries and the singular values of an arbitrary matrix. It is noted in this paper that, based on the induction principle, such a matrix can be constructed numerically by a fast recursive algorithm, provided that the given singular values and diagonal elements satisfy the Sing-Thompson conditions.