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.

K C Sivakumar

Department of Mathematics

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Positivity

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.

Fulltext

Linear Algebra and Its Applications

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

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

In this article, a new characterization for the nonnegativity of Moore-Penrose inverses of Gram operators over Hilbert spaces is presented. The main result generalizes the existing result for invertible Gram operators. © 2008 Birkhäuser Verlag Basel/Switzerland.

A new characterization of nonnegativity of Moore-Penrose inverses of Gram operators

This paper is concerned with necessary and sufficient conditions for the nonnegativity of Moore-Penrose inverses of Gram operators between real Hilbert spaces. These conditions include statements on acuteness (or obtuseness) of certain closed convex cones. The main result generalizes a well known result for inverses in the finite dimensional case over the nonnegative orthant to Moore-Penrose inverses in (possibly) infinite dimensional Hilbert spaces over any general closed convex cone. © 2006 Elsevier Inc. All rights reserved.

Journal	Positivity
ISSN	13851292
Open Access	No