Representations for the Drazin inverse of a modified matrix

Abstract

In this paper expressions for the Drazin inverse of a modified matrix $A-CD^{d}B$ are presented
in terms of the Drazin inverses of $A$ and the generalized Schur complement $D-BA^{d}C$
under fewer and weaker restrictions, which generalizes and unifies several results in the literature and the Sherman-Morrison-Woodbury formula.