New classes of matrix decompositions
Algebraic Geometry
2016-09-30 v2
Abstract
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, extending our work in arXiv:1307.5132. We prove that every matrix is a product of finitely many bidiagonal, skew symmetric (when n is even), generic, companion matrices and generalized Vandermonde matrices, respectively. We also prove that a generic 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.
Cite
@article{arxiv.1605.05626,
title = {New classes of matrix decompositions},
author = {Ke Ye},
journal= {arXiv preprint arXiv:1605.05626},
year = {2016}
}