Weak 1D and D1 inverses
Dijana Mosić, Huihui Zhu · Journal of Algebra and Its Applications · 2024
Our aim is to consider extensions of the systems for defining the 1D, D1, weak MPD and weak DMP inverses using an inner inverse, a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. As unique solutions of new extended systems, we introduce weak 1D and D1 inverses as wider classes of generalized inverses which contain the 1D, D1, inner-CEP, 1WG and inner-[Formula: see text]-WG inverses. We establish characterizations and formulae for weak 1D and D1 inverses. Applying the weak 1D and D1 inverses, solvability of some linear equations is proved. Consequently, a basic result about application of inner inverses for solving linear equations is obtained.