Characterizations of the core inverse and the core partial ordering

Abstract

In this note, we revisit the core inverse and the core partial ordering introduced by Baksalary and Trenkler [Linear Multilinear Algebra. 2010;58:681–697]. We prove that the core inverse of is the unique solution of and , and establish several characterizations of the core inverse, the core partial ordering and the reverse order law for the core inverse.