Stability Matrices and the Solvability of Certain Systems of Linear Inequalities

Research output: Contribution to journalArticle

Abstract

Let A be a real n × n matrix with non-negative non-diagonal elements ai j (i ≠ J). A is called a stability matrix if and only if all of its eigenvalues have strictly negative real parts. It is proved that A is a stability matrix if and only if the system Ax ≽ 0, x ≽ 0 has no non-trivial solution. Further, one and only one of the systems Ax < 0, x > 0 and Ax ≽ 0, x ≽ 0 has a non-trivial solution.

Original languageEnglish (US)
Pages (from-to)253-255
Number of pages3
JournalLinear and Multilinear Algebra
Volume2
Issue number3
DOIs
StatePublished - Jan 1 1974
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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