Stable subspaces of matrix pairs
type: Item
instance of: scholarly article
title: Stable subspaces of matrix pairs
zbMATH Open document ID: 0953.93018
DOI: 10.1016/S0024-3795(99)00164-0
author: Yanyan Li
published in: Linear Algebra and its Applications
publication date: 2001-01-29T00:00:00Z
review text: Let \(A:\mathbb{C}^n\to\mathbb{C}^n\) and \(B:\mathbb{C}^m\to\mathbb{C}^n\) be linear maps. A subspace \({\mathcal N}\subseteq \mathbb{C}^n\) is called \((A,B)\)-invariant, if \(A({\mathcal N}) \subseteq {\mathcal N}+ B(\mathbb{C}^m)\). An \((A,B)\)-invariant subspace is called \((A,B)\)-stable if for any pair \((A',B')\)-close to \((A,B)\) there exists an \((A',B')\)-invariant subspace \({\mathcal N}'\) of \(\mathbb{C}^n\) which is close to \({\mathcal N}\) (say in topology of the corresponding Grassmannian). The authors prove several conditions under which an \((A,B)\)-invariant subspace is acutally \((A,B)\)-stable.
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 15A99
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 1420044
zbMATH Keywords: \((A,B)\) stability
zbMATH Keywords: \((A,B)\) invariance
zbMATH Keywords: structural stability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1420044