On Nonnegative Moore-Penrose Inverses of Perturbed Matrices

Abstract

Nonnegativity of the Moore-Penrose inverse of a perturbation of the form $A-XG{Y}^T$ is considered when $A^{\mathrm{†}}\ge 0$. Using a generalized version of the Sherman-Morrison-Woodbury formula, conditions for ${(A-XG{Y}^T)}^{\mathrm{†}}$ to be nonnegative are derived. Applications of the results are presented briefly. Iterative versions of the results are also studied.