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

Huang, Zejun
; 
Sze, Nung-Sing
; 
Li, Chi-Kwong
; 
Choi, Man-Duen
Abstract
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.
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2012-01-01
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Mathematics
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Mathematics
DOI
10.1016/j.laa.2011.12.010
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https://scholarworks.wm.edu/handle/internal/713
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