Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues

被引：8

作者：

Choi, Man-Duen ^{[3
]}

Huang, Zejun ^{[1
]}

Li, Chi-Kwong ^{[2
]}

Sze, Nung-Sing ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[3] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 09期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Invertible matrices; Diagonal matrices; Distinct eigenvalues;

D O I：

10.1016/j.laa.2011.12.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for every invertible n x n complex matrix A there is an n x n diagonal invertible D such that AD has distinct eigenvalues. Using this result, we affirm a conjecture of Feng, Li, and Huang that an is x is matrix is not diagonally equivalent to a matrix with distinct eigenvalues if and only if it is singular and all its principal minors of size n - 1 are zero. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：3773 / 3776

页数：4

共 4 条

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[4]

Horn R.A., 2012, Matrix Analysis

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