The Equivalence Near-Canonical Form Theorem of a Matrix Triplet Over an Arbitrary Division Ring with Applications

In this paper a theorem concerning the general matrix triplet (, , ) where and are matrices over an arbitrary division ring with compatible dimensions × , × , × , respectively, is given. The equivalence near-canonical form of the matrix triplet () mentioned above is proposed and a practical algorithm for the equivalence near-canonical form of a matrix triplet is also presented. Applications that are investigated include the solution of a system of linear matrix equations over the dependence of the generalized Schur complement over the rank of a partitioned matrix over rank minimization of a partitioned matrix over and the connection with generalized Schur complement