Generalized Drazin inverses of anti-triangular block matrices

In this paper we give formulae for the generalized Drazin inverse M d of an anti-triangular matrix M = ( A B C 0 ) in two different ways: one is to express M d in terms of A d with arbitrary B and C, the other is to express M d in terms of B d and C d with arbitrary A. Moreover, the results are applied to obtain generalized Drazin inverses of various structured matrices and some special cases are analyzed.