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

Subject Areas : Linear and multilinear algebra; matrix theory

M. S. Lone ¹ , T. H. Khan ²

1 - Department of School Education, HSS Razloo, Kund, Kulgam- 192221, JK, India
2 - Department of Higher Education, GDC(A.S.C), Srinagar-190008, JK, India

Received: 2020-08-26 Accepted : 2021-03-11 Published : 2021-03-01

Keywords: singular value decomposition, Minkowski inverse, Range Symmetric, m-projectors, range disjoint, full range,

Abstract :

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.

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