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

Man Duen Choi, Zejun Huang, Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

We show that for every invertible n×n complex matrix A there is an n×n diagonal invertible D such that AD has distinct eigenvalues. Using this result, we affirm a conjecture of Feng, Li, and Huang that an n×n 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.
Original languageEnglish
Pages (from-to)3773-3776
Number of pages4
JournalLinear Algebra and Its Applications
Volume436
Issue number9
DOIs
Publication statusPublished - 1 May 2012

Keywords

  • Diagonal matrices
  • Distinct eigenvalues
  • Invertible matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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