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arXiv · 1506.08962

Product of positive semi-definite matrices

Jianlian Cui·Chi-Kwong Li·Nung-Sing Sze
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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 $k = 1,2,3,4,5$.

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Jianlian Cui, Chi-Kwong Li, Nung-Sing Sze. 2015-06-30. Product of positive semi-definite matrices. https://arxiv.org/abs/1506.08962

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