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The Scientific World Journal
Volume 2013, Article ID 765732, 6 pages
http://dx.doi.org/10.1155/2013/765732
Research Article

Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space

1Department of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Oum-El-Bouaghi University, Oum-El-Bouaghi 04000, Algeria
2Department of Basic Sciences and Humanities, College of Engineering, University of Dammam, P.O. Box 1982, Dammam 34151, Saudi Arabia
3Department of Mathematics, Faculty of Sciences, University of Abant Izzet Baysal, Bolu Turkey, 14280 Bolu, Turkey

Received 9 August 2013; Accepted 18 September 2013

Academic Editors: J. Hoff da Silva and L. Székelyhidi

Copyright © 2013 Hanifa Zekraoui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce some new algebraic and topological properties of the Minkowski inverse of an arbitrary matrix (including singular and rectangular) in a Minkowski space . Furthermore, we show that the Minkowski inverse in a Minkowski space and the Moore-Penrose inverse in a Hilbert space are different in many properties such as the existence, continuity, norm, and SVD. New conditions of the Minkowski inverse are also given. These conditions are related to the existence, continuity, and reverse order law. Finally, a new representation of the Minkowski inverse is also derived.