New classes of matrix decompositions

The idea of decomposing a matrix into a product of structured matrices such as triangular, orthogonal, diagonal matrices is a milestone of numerical computations. In this paper, we describe six new classes of matrix decompositions over complex number field, extending our work in [5]. We prove that every n×n complex matrix is a product of finitely many tridiagonal, skew symmetric (when n is even), companion and generalized Vandermonde matrices, respectively. We also prove that a generic complex n×n centrosymmetric matrix is a product of finitely many symmetric Toeplitz (resp. persymmetric Hankel) matrices. We determine an upper bound of the number of structured matrices needed to decompose a matrix for each case.