The authors revisit the notion of a row monotone matrix and obtain new results that establish relationships with certain specific types of splittings of the matrix concerned. Among other results, analogous results for range monotone matrices are also obtained. © 2011 Elsevier Inc. All rights reserved.

K C Sivakumar

Department of Mathematics

GROUP INVERSE

Monotonicity

MOORE-PENROSE INVERSE

Non-negativity

SPLITTINGS

Linear algebra

Mathematical techniques

Matrix algebra

Fulltext

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IIT Madras

Linear Algebra and Its Applications

The objective of this paper is to study the nonnegativity of the Moore-Penrose inverse of an operator between real Hilbert spaces. A sufficient condition ensuring this is given in terms of certain spectral property of all positive splittings of the given operator. A partial converse is proved. © 2008 Springer Science + Business Media B.V.

Positivity

Nonnegative moore-penrose inverses of operators over Hilbert spaces

Operators and Matrices

On splittings of matrices and nonnegative generalized inverses

Mathematische Nachrichten

On positive invertibility of operators and their decompositions

Positive Invertibility of Nonselfadjoint Operators

Springer Series in Computational Mathematics

Matrix Iterative Analysis

Generalizations of matrix monotonicity and their relationships with certain subclasses of proper splittings

Journal	Linear Algebra and Its Applications
ISSN	00243795
Open Access	Yes