Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic Lyapunov equation of general inertia were studied in (N. Cohen, I. Lewkowicz, Linear Algebra and its Appl. 250 (1997) 105-131). Here, in the price of doubling the size of the matrices involved, we introduce a unified framework for the equations of Sylvester, Lyapunov and Riccati. This enables one to extend the convex invertible cone structure to all these three equations and explore related properties. In particular, the use of the Matrix Sign Function for solving these equations is examined.

Original languageEnglish
Pages (from-to)107-133
Number of pages27
JournalLinear Algebra and Its Applications
Volume286
Issue number1-3
DOIs
StatePublished - 1 Jan 1999

Fingerprint

Dive into the research topics of 'Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati'. Together they form a unique fingerprint.

Cite this