Document Type
Article
Department/Program
Mathematics
Journal Title
Linear Algebra and Its Applications
Pub Date
2012
Volume
436
Issue
9
First Page
3773
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.
Recommended Citation
Huang, Zejun; Sze, Nung-Sing; Li, Chi-Kwong; and Choi, Man-Duen, Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues (2012). Linear Algebra and Its Applications, 436(9), 3773-3776.
10.1016/j.laa.2011.12.010
DOI
10.1016/j.laa.2011.12.010
