Representations for the Drazin Inverse of a Modified Matrix


Daochang Zhang, Xiankun Du




In this paper expressions for the Drazin inverse of a modified matrix $A-CD^dB$ are presented in terms of the Drazin inverses of $A$ and the generalized Schur complement $D-BA^dC$ under weaker restrictions. Our results generalize and unify several results in the literature and the Sherman--Morrison--Woodbury formula.