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

The m-core-EP inverse in Minkowski space