Nonnegativity of the Moore-Penrose inverse of a perturbation of the form A-XGYT is considered when A†≥0. Using a generalized version of the Sherman-Morrison-Woodbury formula, conditions for (A-XGYT) † to be nonnegative are derived. Applications of the results are presented briefly. Iterative versions of the results are also studied. © 2013 Shani Jose and K. C. Sivakumar.

K C Sivakumar

Department of Mathematics

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On Nonnegative Moore-Penrose Inverses of Perturbed Matrices

Journal of Applied Mathematics

For A,B∈Rm×n, let J=[A,B] be the set of all matrices C such that A≤C≤B, where the order is component wise. Krasnosel'skij et al. [9] and Rohn [11] have shown that if A and B are invertible with A- 1≥0 and B-1≥0, then every C∈J is invertible with C-1≥0. In this article, we present certain extensions of this result to the singular case, where the nonnegativity of the usual inverses is replaced by the nonnegativity of the Moore-Penrose inverse. © 2011 Elsevier Inc. All rights reserved.

Linear Algebra and Its Applications

Moore-Penrose inverse positivity of interval matrices

In this article, a classical result of Cottle and Veinott characterizing least elements of polyhedral sets in terms of nonnegative left-inverses is extended to characterize nonnegativity of some of the most important generalized inverses. We also present generalizations of the other results of these authors for the case of the Moore-Penrose inverse. © 2011 Published by Elsevier Inc.

Nonnegative generalized inverses and least elements of polyhedral sets

Operators and Matrices

On splittings of matrices and nonnegative generalized inverses

Applied Mathematics Letters

A generalization of the Sherman–Morrison–Woodbury formula

Linear Algebra and its Applications

Some results on structured M-matrices with an application to wireless communications

On nonnegative moore-penrose inverses of perturbed matrices

Journal	Journal of Applied Mathematics
ISSN	1110757X
Open Access	Yes