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

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

We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ in a Hilbert spac...

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Main Authors: Hanifa Zekraoui, Zeyad Al-Zhour, Cenap Özel
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2013/765732
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spelling doaj-2d12f88b3db94744b15d50dd201f4ba62020-11-25T00:16:04ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/765732765732Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski SpaceHanifa Zekraoui0Zeyad Al-Zhour1Cenap Özel2Department of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Oum-El-Bouaghi University, Oum-El-Bouaghi 04000, AlgeriaDepartment of Basic Sciences and Humanities, College of Engineering, University of Dammam, P.O. Box 1982, Dammam 34151, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, University of Abant Izzet Baysal, Bolu Turkey, 14280 Bolu, TurkeyWe introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ 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 A⊕ is also derived.http://dx.doi.org/10.1155/2013/765732
collection DOAJ
language English
format Article
sources DOAJ
author Hanifa Zekraoui
Zeyad Al-Zhour
Cenap Özel
spellingShingle Hanifa Zekraoui
Zeyad Al-Zhour
Cenap Özel
Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
The Scientific World Journal
author_facet Hanifa Zekraoui
Zeyad Al-Zhour
Cenap Özel
author_sort Hanifa Zekraoui
title Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
title_short Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
title_full Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
title_fullStr Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
title_full_unstemmed Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
title_sort some new algebraic and topological properties of the minkowski inverse in the minkowski space
publisher Hindawi Limited
series The Scientific World Journal
issn 1537-744X
publishDate 2013-01-01
description We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ 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 A⊕ is also derived.
url http://dx.doi.org/10.1155/2013/765732
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AT zeyadalzhour somenewalgebraicandtopologicalpropertiesoftheminkowskiinverseintheminkowskispace
AT cenapozel somenewalgebraicandtopologicalpropertiesoftheminkowskiinverseintheminkowskispace
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