The C-S Inverse and Its Applications

Abstract

In this paper, we introduce a generalized core inverse (called the C-S inverse) and give some properties and characterizations of the inverse. By applying the C-S inverse, we introduce a binary relation (denoted “ {mathop le limits ^{textcircled {S}}} ”) and a partial order (called the C-S partial order and denoted “ {mathop le limits ^{textcircled {{c!s}}}} ”), study their properties and consider the relationship between them and some classical partial orders. At last, by applying the C-S inverse, we give some characterizations of the EP matrix and i-EP matrix.