On （B,C）-MP- inverses of complex matrices

Abstract

For any $A \in \mathbb{C}^{n\times m}$, the set of all $n$ by $m$ complex matrices, Mosi\'{c} and Stanimirovi\'{c} \cite{Mosic2021} introduced the composite OMP inverse of $A$ by its outer inverse with the prescribed range, null space and Moore-Penrose inverse. This inverse unifies the core inverse, DMP inverse and Moore-Penrose inverse. In this paper, we mainly introduce and investigate a class of generalized inverses in complex matrices. Also, it is proved that this generalized inverse coincides with the OMP inverse. Finally, the defined inverse is related to OMP-inverses, $W$-core inverses and $(b,c)$-core inverses in the context of matrices.