The m-MP weak core inverse and its applications

Abstract

In this paper, we introduce a new generalized inverse called m-MP weak core inverse by using the m-core-nilpotent decomposition. This newly generalized inverse unifies the CMP inverse and MP weak core inverse. We characterize the m-MP weak core inverse by ranges, null spaces and matrix equations. Moreover, we present the integral and limit representations for the m-MP weak core inverse. Furthermore, we give the applications of the m-MP weak core inverse in solving a system of linear equations.