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

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