Nonnegativity Preservation under Singular Values Perturbation
Emedin Montaño, Mario Salas, Ricardo L. Soto · Mathematical Problems in Engineering · 2009
We study how singular values and singular vectors of a matrix A change, under matrix perturbations of the form and , 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.