Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773342 | Linear Algebra and its Applications | 2017 | 8 Pages |
Abstract
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product. However, the characterizations of matrices that require three or four positive semi-definite matrices in the product are lacking. In this paper, we give a complete characterization of these two types of matrices. With these results, we give an algorithm to determine whether a square matrix can be expressed as the product of k positive semi-definite matrices but not fewer, for k=1,2,3,4,5.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jianlian Cui, Chi-Kwong Li, Nung-Sing Sze,