Generalized core inverses of matrices

Abstract

In this paper, we introduce two new generalized inverses of matrices, namely, the $⟨i|m$-core inverse and the $\pare{j}{m}$-core inverse. The $⟨i|m$-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler \cite{BT} and the core-EP inverse defined by Manjunatha Prasad and Mohana \cite{MM}. The $\pare{j}{m}$-core inverse of a complex matrix extends the notions of the core inverse and the $\mathrm{DMP}$-inverse defined by Malik and Thome \cite{MT}. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers.

19 pages