  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.
