Characterization of matrices using m-projectors and singular value decomposition in Minkowski space

Journal of Linear and Topological Algebra

دوره 10، شماره 01، خرداد 2021، صفحه 43-58   

نوع مقاله: Research Paper

نویسندگان

M. S. Lone^{* 1}؛ T. H. Khan²

¹Department of School Education, HSS Razloo, Kund, Kulgam- 192221, JK, India

²Department of Higher Education, GDC(A.S.C), Srinagar-190008, JK, India

چکیده

In this paper we characterize different classes of matrices in Minkowski space $\mathcal{M}$ by generalizing the singular value decomposition in terms of \emph{m}-projectors. Furthermore, we establish results on the relation between the range spaces and rank of the range disjoint matrices by utilizing the singular value decomposition obtained in terms of \emph{m}-projectors. Since there is no result on the formulation of Minkowski inverse of the sum of two matrices, we have established an expression for the Minkowski inverse of the sum of a range disjoint matrix with its Minkowski adjoint, which will ease to formulate an expression for the Minkowski inverse of the sum of two matrices in general case.

کلیدواژه‌ها

Singular value decomposition؛ range symmetric؛ Minkowski Inverse؛ m-projectors؛ range disjoint؛ full range

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