Products of positive semi-definite matrices

Jianlian Cui, Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)17-24
Number of pages8
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 Sept 2017


  • Numerical range
  • Positive semi-definite matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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