On strictly positively invariant cones
type: Item
instance of: scholarly article
title: On strictly positively invariant cones
zbMATH Open document ID: 0537.15013
DOI: 10.1016/0024-3795(82)90095-7
published in: Linear Algebra and its Applications
publication date: 1982-01-01T00:00:00Z
review text: The main result is the following: Let A be a real \(n\times n\) matrix and C a proper closed convex cone in \({\mathbb{R}}^ n\) such that \(e^{tA}(C\backslash \{0\})\subseteq int(C)\) for all positive t. Then the boundary of the set of points with the property that the image under the action of \(e^{tA}\) is in C for some positive t is an (n-1)- dimensional A-invariant subspace. This is applied to stability of cones.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 3853284
zbMATH Keywords: strict positive invariance
zbMATH Keywords: direct sum decomposition
zbMATH Keywords: matrix exponentials
zbMATH Keywords: invariant cone
zbMATH Keywords: invariant subspace
zbMATH Keywords: stability
author: R. J. Stern
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
full work available at URL: 0024-3795(82)90095-7
OpenAlex ID: W2055997526
cites work: Quasimonotonie und Ungleichungen in halbgeordneten Räumen
cites work: Q4067388
cites work: Cross-Positive Matrices
cites work: Generalized M-matrices
cites work: Spectral Properties of Matrices which have Invariant Cones
cites work: Q5342712
description: scientific article; zbMATH DE number 3853284