The m-core-EP inverse in Minkowski space

Abstract

In this paper, we introduce the m-core-EP inverse in Minkowski space, consider its properties, and get several sufficient and necessary conditions for the existence of the m-core-EP inverse. We give the m-core-EP decomposition in Minkowski space, and note that not every square matrix has the decomposition. Furthermore, by applying the m-core-EP inverse and the m-core-EP decomposition, we introduce the m-core-EP order and give some characterizations of it.