Copyright © 2009 Emedin Montaño et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study how singular values and singular vectors of a matrix A change, under matrix perturbations of the form A+αuivi∗ and A+αupvq∗, p≠q, where α∈ℝ, A is an m×n positive matrix with singular values σ1≥σ2≥⋯≥σr>0,r=min⁡{m,n}, and uj,vk, j=1,…,m;k=1,…,n, are the left and right singular vectors, respectively. In particular we give conditions under which this kind of perturbations preserve nonnegativity and certain matrix structures.