A pair of matrices sharing common Lyapunov solutions - A closer look

Nir Cohen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Let A,B be a pair of matrices with regular inertia. If HA+A *H and HB+B *H are both positive definite for some Hermitian matrix H then all matrices in conv(A,A -1,B,B -1) have identical regular inertia. This, in turn, implies that both conv(A,B) and conv(A,B -1) consist of non-singular matrices. In general, neither of the converse implications holds. In this paper we seek situations where they do hold, in particular, when A and B are real 2×2 matrices. Several aspects of the above statements for n×n matrices are discussed. A connection to the characterization of the convex hull of matrices with regular inertia is introduced. Differences between the real and the complex case are indicated.

Original languageEnglish
Pages (from-to)83-104
Number of pages22
JournalLinear Algebra and Its Applications
StatePublished - 1 Feb 2003


  • Convex invertible cones
  • Convex sets of matrices with regular inertia
  • Lyapunov matrix inclusion

ASJC Scopus subject areas

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


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