Left and right W-weighted G-Drazin inverses and new matrix partial orders - Ferreyra, David Eduardo (2025)
This paper investigates a way to define left and right versions of the class of G-Drazin inverses forcomplex rectangular matrices. More precisely, the concepts of W-weighted left (resp. right) G-Drazininverses are introduced and characterized by means of a simultaneous core-nilpotent decomposition as well as by certain system of matrix equations. Then, new partial orders associated with these weighted generalized inverses are presented and studied.