Convex invertible cones and positive real analytic functions
type: Item
instance of: scholarly article
title: Convex invertible cones and positive real analytic functions
zbMATH Open document ID: 1133.15018
author: Nir Cohen
author: Izchak Lewkowicz
published in: Linear Algebra and its Applications
publication date: 2007-08-27T00:00:00Z
review text: The authors investigate and compare convex invertible cones in a matrix algebra and in an algebra of real-analytic weakly stable functions. The main outcome of this analysis is that there exists a considerable number of similar features of convex invertible cones in both spaces. This similarity is demonstrated in many ways in particular in terms of generating elements. The obtained results are nicely illustrated by the numerous examples.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 47L07
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 94C05
zbMATH DE Number: 5183347
zbMATH Keywords: convex invertible cones
zbMATH Keywords: positive real functions
zbMATH Keywords: Lyapunov matrix inclusion
zbMATH Keywords: matrix algebra
reviewed by: Alexander Guterman
MaRDI profile type: Publication
full work available at URL: j.laa.2007.04.023
OpenAlex ID: W1993894020
cites work: Q4537717
cites work: Set of matrices with common Lyapunov solution
cites work: Sets of matrices with common Stein solutions and \(H\)-contractions
cites work: Interpolation of rational matrix functions
cites work: Q5560003
cites work: On Realizations of Rational Matrix Functions of Several Complex Variables
cites work: Inertia theorems for matrices: the semidefinite case
cites work: A Generalization of the Inertia Theorem
cites work: Convex invertible cones and the Lyapunov equation
cites work: Convex invertible cones of state space systems.
cites work: A characterization of convex cones of matrices with constant regular inertia
cites work: A pair of matrices sharing common Lyapunov solutions--A closer look
cites work: Q3922907
cites work: Q3704135
cites work: Q4040931
cites work: The matrix sign function
cites work: Convex invertible cones of matrices -- a unified framework for the equations of Sylvester, Lyapunov and Riccati
cites work: Convex invertible sets and matrix sign function
cites work: Inverse closed ray-nonsingular cones of matrices
cites work: An inertia theorem for Lyapunov's equation and the dimension of a controllability space
cites work: Q5684916
cites work: Q5622052
cites work: Interpolation with positive-real functions
DOI: 10.1016/J.LAA.2007.04.023
description: scientific article; zbMATH DE number 5183347