The distribution of eigenvalues of doubly cyclic Z+-matrices

Charles R. Johnson, Zachary Price, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


It is shown that every matrix in a large class of n-by-n doubly cyclic Z+ matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.

Original languageEnglish (US)
Pages (from-to)3576-3580
Number of pages5
JournalLinear Algebra and Its Applications
Issue number11
StatePublished - Dec 1 2013


  • Doubly-cyclic Z matrices
  • Eigenvalue location

ASJC Scopus subject areas

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


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