On the Lipschitz stability of (A, B)-invariant subspaces

被引：0

作者：

Puerta, Ferran ^{[1
]}

Puerta, Xavier ^{[1
]}

机构：

[1] ETSEIB UPC, Dept Matemat Aplicada 1, Barcelona, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 01期

关键词：

(A; B)-invariant subspace; Lipschitz stability; INVARIANT SUBSPACES; PAIRS;

D O I：

10.1016/j.laa.2012.07.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be the set of triples (A, B, S) where S is an (A, B)-invariant subspace and let F-mu be the matrix having minimum norm such that (A + BF mu)(S) subset of S. Then, if theta : T -> M-m,M-n is the map defined by theta(A, B, S) = F-mu and theta is continuous at (A, B, S) a simple necessary and sufficient condition is given for the Lipschitz stability of S. It is shown that this continuity condition is satisfied in an open and dense subset of T and that the set of triples (A, B, S) such that S is Lipschitz stable is also open and dense in T. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：182 / 190

页数：9

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