Representations for the Drazin inverse of the generalized Schur complement

Abstract

In this paper we present expressions for the Drazin inverse of the generalized Schur complement $A-C{D}^{d}B$ in terms of the Drazin inverses of $A$ and the generalized Schur complement $D-B{A}^{d}C$ under less and weaker restrictions, which generalize several results in the literature and the formula of Sherman-Morrison-Woodbury type.