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.

K C Sivakumar

Department of Mathematics

Computational complexity

Linear algebra

Optimization

Problem solving

GRAM OPERATOR

MOORE-PENROSE INVERSES

OBTUSE CONES

Mathematical operators

Fulltext

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IIT Madras

Linear Algebra and Its Applications

This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian © Springer International Publishing Switzerland 2016.

Infinite Matrices and Their Recent Applications

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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 paper, we derive necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a Gram matrix defined in an indefinite inner product space using indefinite matrix multiplication. These conditions include the acuteness of a pair of closed convex cones. © 2008 Springer Science+Business Media, LLC.

Journal of Optimization Theory and Applications

Nonnegative Moore-Penrose inverse of Gram matrices in an indefinite inner product space

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.

Positivity

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

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.

Nonnegative moore-penrose inverses of operators over Hilbert spaces

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Linear Algebra and its Applications

Obtuse cones and Gram matrices with nonnegative inverse

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Nonnegative Moore-Penrose inverses of Gram operators

Journal	Linear Algebra and Its Applications
ISSN	00243795
Open Access	Yes