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On the {2}-inverse and some ordering properties of nonnegative definite matrices

On the {2}-inverse and some ordering properties of nonnegative definite matrices An inverseG of a given matrixA satisfying the conditionGAG=G is known as a {2}-inverse ofA. This paper makes the {2}-inverse the starting point for studying the Löwner partial ordering of real nonnegative matrices. Simple basic properties of the {2}-inverses yield various extensions for the reverse ordering property,A≥B if and only ifB −1≥A −1, of the positive definite matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On the {2}-inverse and some ordering properties of nonnegative definite matrices

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References (13)

Publisher
Springer Journals
Copyright
Copyright © 1996 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009557
Publisher site
See Article on Publisher Site

Abstract

An inverseG of a given matrixA satisfying the conditionGAG=G is known as a {2}-inverse ofA. This paper makes the {2}-inverse the starting point for studying the Löwner partial ordering of real nonnegative matrices. Simple basic properties of the {2}-inverses yield various extensions for the reverse ordering property,A≥B if and only ifB −1≥A −1, of the positive definite matrices.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 14, 2005

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