G-Drazin inverse combined with inner inverse
Gayatri Maharana, Jajati Keshari Sahoo, Néstor Thome · Linear and Multilinear Algebra · 2024
This article introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition. Further, we introduce a binary relation for GD1 inverse and 1GD inverse, along with a few derived properties.