When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix

Charles R. Johnson, Sivaram K. Narayan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

An n-by-n real matrix A enjoys the "leading implies all" (LIA) property, if, whenever D is a diagonal matrix such that A+D has positive leading principal minors (PMs), all PMs of A are positive. Symmetric and Z-matrices are known to have this property. We give a new class of matrices ("mixed matrices") that both unifies and generalizes these two classes and their special diagonal equivalences by also having the LIA property. "Nested implies all" (NIA) is also enjoyed by this new class.

Original languageEnglish
Pages (from-to)2934-2947
Number of pages14
JournalLinear Algebra and Its Applications
Volume439
Issue number10
DOIs
StatePublished - Nov 15 2013

Keywords

  • Leading principal minors
  • M-matrix
  • Nested sequence of principal minors
  • Positive definite
  • Symmetric
  • Z-matrix

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