Characterization of matrices using m-projectors and singular value decomposition in Minkowski space
محورهای موضوعی : Linear and multilinear algebra; matrix theory
M. S. Lone
1
(Department of School Education, HSS Razloo, Kund, Kulgam- 192221, JK, India)
T. H. Khan
2
(Department of Higher Education, GDC(A.S.C), Srinagar-190008, JK, India)
کلید واژه: singular value decomposition, Minkowski inverse, Range Symmetric, m-projectors, range disjoint, full range,
چکیده مقاله :
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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