Local and global reducibility of spaces of nilpotent matrices

被引：0

作者：

Mastnak, Mitja ^{[1
]}

Omladic, Matjaz ^{[2
]}

Radjavi, Heydar ^{[3
]}

Sivic, Klemen ^{[4
]}

机构：

[1] St Marys Univ, Dept Math, Halifax, NS, Canada

[2] Inst Math Phys & Mech, Ljubljana, Slovenia

[3] Univ Waterloo, Dept Pure Math, Waterloo, ON, Canada

[4] Univ Ljubljana, Dept Math, Ljubljana, Slovenia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 611卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Linear spaces of nilpotent matrices; Reducibility; Triangularizability; Order of nilpotency; Compact operators; Quasinilpotent operators;

D O I：

10.1016/j.laa.2020.10.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We explore the relationship between local and global reducibility of spaces of nilpotent matrices. By local reducibility we mean that small subspaces of a given irreducible linear space L subset of M-n (C) are reducible. One of our main results is that for certain integers m depending on n there is an (m+1)-dimensional space L which is irreducible, but every one of its m-dimensional subspaces is, not just reducible, but simultaneously triangularizable. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：260 / 278

页数：19

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