Core-EP-Nilpotent Decomposition and Its Applications

Abstract

We give the illustration of a new decomposition: the core-EP-nilpotent decomposition, which is on the basis of the core-EP decomposition and EP-nilpotent decomposition for some square matrices in this thesis. According to the new decomposition, we show the definitions and characteristics of two new orders: core-E-N partial order and core-E-S partial order. We also illustrate relations of the two orders under some restricted conditions.