A note on numerical range and product of matrices

被引：5

作者：

Cheng, Che-Man ^{[1
]}

Gao, Yuan ^{[1
]}

机构：

[1] Univ Macau, Dept Math, Macao, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 07期

关键词：

Spectrum; Numerical range;

D O I：

10.1016/j.laa.2012.12.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be any n x n complex matrix. Let sigma (A) and W (A) denote respectively the spectrum and the numerical range of A. It is wellknown that if A is a multiple of a positive semidefinite matrix, then sigma(AB) subset of W (A)W(B) for all n x n complex matrices B. We show that the converse is also true. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3139 / 3143

页数：5