characterization of matrices using m-projectors and singular value decomposition in minkowski space

In this paper we characterize different classes of matrices in minkowski space m by generalizing the singular value decomposition in terms of 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 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.