Explicit representations of the Drazin inverse of block matrix and modified matrix
Dragana S. Cvetković‐Ilić, Jianbiao Chen, Zhaoliang Xu · Linear and Multilinear Algebra · 2008
A new result on the Drazin inverse of 2 × 2 block matrix , where A and C are square matrices are presented, extended in the case when D = 0, the well-known representation for the Drazin inverse of M, given by Hartwig, Meyer and Rose in 1977, respectively. Using that new result, an explicit representation for the Drazin inverse of a modified matrix P + RS and its generalized matrix PQ + RS are also presented.