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.

K C Sivakumar

Department of Mathematics

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Journal of Optimization Theory and Applications

Fulltext

Theorems of the alternative over indefinite inner product spaces

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.

Linear Algebra and Its Applications

Nonnegative Moore-Penrose inverses of Gram operators

In this short note, we present a simple linear-algebraic proof, by verification, of the well-known Greville/Udwadia/Kalaba formula for computing the Moore-Penrose inverse of a matrix. © 2006 Springer Science + Business Media, Inc.

Journal	Journal of Optimization Theory and Applications
ISSN	00223239
Open Access	No