The C-S Inverse and Its Applications
Hongxing Wang, Na Liu · Bulletin of the Malaysian Mathematical Sciences Society · 2023
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 “ $${\mathop \le \limits ^{\textcircled {S}}}$$ ≤ S ”) and a partial order (called the C-S partial order and denoted “ $${\mathop \le \limits ^{\textcircled {{c\!s}}}}$$ ≤ 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.