Products of positive semi-definite matrices

Jianlian Cui Department of Mathematics, Tsinghua University, Chi-KwongLi Department of Mathematics, College of William and Mary Nung-SingSze Department of Applied Mathematics, The Hong Kong Polytechnic University

General Mathematics mathscidoc:1611.13002

Linear Algebra and its Applications, 2016
It is known that every complex square matrix with nonnega-tive 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 kpositive semi-definite matrices but not fewer, for k=1, 2, 3, 4, 5.
Positive semi-definite matrices;Numerical range
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@inproceedings{jianlian2016products,
  title={Products of positive semi-definite matrices},
  author={Jianlian Cui, Chi-KwongLi, and Nung-SingSze},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161125162029329702642},
  booktitle={Linear Algebra and its Applications},
  year={2016},
}
Jianlian Cui, Chi-KwongLi, and Nung-SingSze. Products of positive semi-definite matrices. 2016. In Linear Algebra and its Applications. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161125162029329702642.
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