Spectral properties of sign symmetric matrices

Daniel Hershkowitz, Nathan Keller

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Spectral properties of sign symmetric matrices are studied. A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which complex numbers can serve as eigenvalues of sign symmetric 3 × 3 matrices. The results are applied in the discussion of the eigenvalues of QM-matrices. In particular, it is shown that for every positive integer n there exists a QM-matrix A such that A k is a sign symmetric P-matrix for all k ≤ n, but not all the eigenvalues of A are positive real numbers.

Original languageEnglish
JournalElectronic Journal of Linear Algebra
Volume13
DOIs
StatePublished - 11 Mar 2005
Externally publishedYes

Keywords

  • Basic circulant permutation matrices
  • Circulant matrices
  • P-matrices
  • PM-matrices
  • Q-matrices
  • QM-matrices
  • Sign symmetric matrices
  • Spectrum

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