On the Drazin inverse of block matrices and generalized Schur complement

In this paper, we give an additive result for the Drazin inverse with its applications, we obtain representations for the Drazin inverse of a 2 × 2 complex block matrix having generalized Schur complement S=D-CADBS=D-CADB equal to zero or nonsingular. Several situations are analyzed and recent results are generalized [R.E. Hartwig, X. Li, Y. Wei, Representations for the Drazin inverse of a 2×22×2 block matrix, SIAM J. Matrix Anal. Appl. 27 (3) (2006) 757–771].