the Drazin inverse matrix modification formulae with Peirce corners
Abstract
Our motivation is to derive the Drazin inverse matrix modification formulae utilizing the Drazin inverses of adequate Peirce corners
under some special cases, and the Drazin inverse of a special
matrix with an additive perturbation. As applications, several new
results for the expressions of the Drazin inverses of modified
matrices $A-CB$ and $A-CD^{d}B$ are obtained, and some well known results in the literature, as the Sherman-Morrison-Woodbury
formula and Jacobson's Lemma, are generalized.
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