title: Some new algebraic and topological properties of the Minkowski inverse in the Minkowski space.
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.
authors.affiliation: Department of Mathematics and Informatic, Faculty of Exact and Natural Sciences, Oum-El-Bouaghi University, Oum-El-Bouaghi 04000, Algeria.
authors.forename: Hanifa
authors.initials: H
authors.lastname: Zekraoui
authors.forename: Zeyad
authors.initials: Z
authors.lastname: Al-Zhour
authors.forename: Cenap
authors.initials: C
authors.lastname: Özel
mesh_terms: D055641:Mathematical Concepts