Positivity of principal minors, sign symmetry and stability

Daniel Hershkowitz, Nathan Keller

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The relation between positivity of principal minors, sign symmetry and stability of matrices is studied. It is shown that for sign symmetric matrices, having positive principal minors is equivalent to stability, to D-stability, and to having a positive scaling into a stable matrix. The relation between spectra of matrices some of whose powers have positive principal minors and matrices whose corresponding powers have positive sums of principal minors of each order is studied as well. It is shown that for matrices of order less than 4 these two classes share the same spectra. The relation of these classes and stability is studied, in particular for sign symmetric matrices and for anti-sign symmetric matrices.

Original languageEnglish
Pages (from-to)105-124
Number of pages20
JournalLinear Algebra and Its Applications
StatePublished - 1 May 2003
Externally publishedYes


  • D-stability
  • P-matrix
  • P-matrix powers
  • Q-matrix
  • Semistable matrix
  • Sign symmetric matrix
  • Stable matrix
  • Weakly sign symmetric matrix


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