Improved results on the Drazin inverse of a 2 x 2 block matrix in terms of Banachiewicz-Schur forms
Xifu Liu, Hu Yang · Filomat · 2013
In this paper, we derive a representation for the Drazin inverse of a block matrix M = under the assumptions AAπB = 0, CAπB = 0, AADBSSπ = 0, SSDCWAAD(AW)π = 0 and (AW)πAADBSSD = 0, where S = D - CADB is the generalized Schur complement. And the representation can be regarded as an unified form of MD because it covers the case either S is nonsingular or zero. Moreover, some alternative representations for the Drazin inverse are presented. Several situations are analyzed and recent results are generalized.