The Drazin inverse of the sum of four matrices and its applications
Daochang Zhang, Dijana Mosić, Li Guo · Linear and Multilinear Algebra · 2018
Our aim is to establish relations between the Drazin inverses of the pesudo-block matrix (P,Q,R,S) and the block matrix PRSQ, where R2=S2=0. Based on the relations, we give representations for the Drazin inverse of the sum P + Q + R + S under mild restrictions. As the applications, several expressions for the Drazin inverse of a 2×2 block matrix are presented under some assumptions. Our results generalize several results in the literature.