On the existence of group inverses of Peirce corner matrices

Abstract

We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a 2 ×2 block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of the generalized Schur complements and the 2 × 2 block matrix are obtained and some of them generalize several results in the literature.2000 Mathematics Subject Classification. 15A09; 15A30; 65F20.

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