Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/76007
Title: Products of positive semi-definite matrices
Authors: Cui, JL
Li, CK
Sze, NS 
Keywords: Positive semi-definite matrices
Numerical range
Issue Date: 2017
Publisher: North-Holland
Source: Linear algebra and its applications, 2017, v. 528, special issue SI, p. 17-24 How to cite?
Journal: Linear algebra and its applications 
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.
URI: http://hdl.handle.net/10397/76007
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2015.09.045
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