Linear maps on Mn (C) preserving the local spectrum

被引：37

作者：

Gonzalez, Manuel

Mbekhta, Mostafa ^{[1
]}

机构：

[1] Univ Lille 1, UFR Math, F-59655 Villeneuve Dascq, France

[2] Univ Cantabria, Fac Ciencias, Dept Math, E-39071 Santander, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 427卷 / 2-3期

关键词：

linear maps preserving the local spectrum;

D O I：

10.1016/j.laa.2007.07.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let x(0) is an element of C-n be a nonzero vector. We prove that if a linear map phi : M-n (C) -> M-n (C) preserves the local spectrum at x(0); i.e., sigma(T) (x(0)) = sigma(phi(T)) (x(0)) for all T is an element of M-n (C), then there exists an invertible matrix A such that A(x(0)) = x(0) and phi(T) = AT A(-1) for every T. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：176 / 182

页数：7

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