Nonnegativity Preservation under Singular Values Perturbation

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, res...

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Bibliographic Details
Published in:Mathematical problems in engineering 2009, Vol.2009 (2009), p.1-25
Main Authors: Montaño, Emedin, Soto Montero, Ricardo L., Salas, Mario
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1024-123X
1563-5147