From the point of view of generalizations, the core inverse of a matrix has received a lot of attention of researchers in this area resulting in many generalizations of the core inverse, like core-...

In this paper we extend the definition of BT inverse of square complex matrices to rectangular matrices. This new generalized inverse (called the W -weighted BT inverse) always exists and is unique...

Let $A$ and $E$ be $n \times n$ given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by $AXA=AEA$ and $A^k E A X = X A E A^k$, for $k$ being the index of $A$. In addition, its general solution is derived in terms of a G-Drazin inverse of $A$. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.