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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/765732 |
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| author | Hanifa Zekraoui Zeyad Al-Zhour Cenap Özel |
| author_facet | Hanifa Zekraoui Zeyad Al-Zhour Cenap Özel |
| author_sort | Hanifa Zekraoui |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-2d12f88b3db94744b15d50dd201f4ba6 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-2d12f88b3db94744b15d50dd201f4ba62025-02-03T06:01:36ZengWileyThe 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2013/765732 |
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