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. Manuscript profile