Nonnegativity Preservation under Singular Values Perturbation

Abstract EN

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.