Possible inertia combinations in the Stein and Lyapunov equations
type: Item
instance of: scholarly article
title: Possible inertia combinations in the Stein and Lyapunov equations
zbMATH Open document ID: 0827.15011
DOI: 10.1016/0024-3795(93)00296-C
author: Charles R. Johnson
author: Luz Maria DeAlba
published in: Linear Algebra and its Applications
publication date: 1995-11-26T00:00:00Z
review text: The authors consider the Stein equation \(K - AKA^* = H\) (which arises in the study of discrete-time dynamical systems) and the Lyapunov equation \(KA + A^*K = H\) (which arises in the analysis of continuous- time dynamical systems). For these it is shown that the only joint constraints on the inertias of the three matrices are the classical definiteness and semidefiniteness constraints and a simple rank-related constraint.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C99
zbMATH DE Number: 778242
zbMATH Keywords: Stein equation
zbMATH Keywords: discrete-time dynamical systems
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: continuous-time dynamical systems
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
cites work: Rank and inertia bounds for matrices under \(R (AH) \geq 0\)
cites work: Inertia theorems for matrices: the semidefinite case
cites work: Q3998992
cites work: Q4040931
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: Some theorems on the inertia of general matrices
cites work: A Generalization of a Theorem of Lyapunov
full work available at URL: 0024-3795(93)00296-c
OpenAlex ID: W2040369882
Wikidata QID: Q127646989
description: scientific article; zbMATH DE number 778242