The Drazin inverse matrix modification formulae with Peirce corners
Daochang Zhang, Dijana Mosić, Jianping Hu · Filomat · 2021
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 ?? CDdB are obtained, and some well known results in the literature, as the Sherman-Morrison-Woodbury formula and Jacobson?s Lemma, are generalized.