Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598388 | Linear Algebra and its Applications | 2017 | 35 Pages |
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 over complex number field, extending our work in [5]. We prove that every nÃn 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 nÃn 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ke Ye,