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Zekraoui H, Al-Zhour Z, Özel C. Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space. ScientificWorldJournal. 2013;2013:765732doi: 10.1155/2013/765732.
Zekraoui, H., Al-Zhour, Z., & Özel, C. (2013). Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space. TheScientificWorldJournal, 2013765732. https://doi.org/10.1155/2013/765732
Zekraoui, Hanifa, et al. "Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space." TheScientificWorldJournal vol. 2013 (2013): 765732. doi: https://doi.org/10.1155/2013/765732
Zekraoui H, Al-Zhour Z, Özel C. Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space. ScientificWorldJournal. 2013 Oct 29;2013:765732. doi: 10.1155/2013/765732. eCollection 2013. PMID: 24288506; PMCID: PMC3830776.
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ScientificWorldJournal. 2013 Oct 29;2013:765732. doi: 10.1155/2013/765732. eCollection 2013.

Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space.

TheScientificWorldJournal

Hanifa Zekraoui, Zeyad Al-Zhour, Cenap Özel

Affiliations

  1. Department of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Oum-El-Bouaghi University, Oum-El-Bouaghi 04000, Algeria.

PMID: 24288506 PMCID: PMC3830776 DOI: 10.1155/2013/765732

Abstract

We introduce some new algebraic and topological properties of the Minkowski inverse A([Symbol: see text) of an arbitrary matrix A[Symbol: see text] M m,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A ([Symbol: see text]) 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 ([Symbol: see text]) is also derived.

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