Drazin inverse of partitioned matrices in terms of Banachiewicz–Schur forms

N. Castro-González, M.F. Martínez-Serrano
2010 Linear Algebra and its Applications  
Let M = A B C D be a partitioned matrix, where A and D are square matrices. Denote the Drazin inverse of A by A D . The purpose of this paper is twofold. Firstly, we develop conditions under which the Drazin inverse of M having generalized Schur complement, S = D − CA D B, group invertible, can be expressed in terms of a matrix in the Banachiewicz-Schur form and its powers. Secondly, we deal with partitioned matrices satisfying rank(M) = rank(A D ) + rank(S D ), and give conditions under which
more » ... he group inverse of M exists and a formula for its computation.
doi:10.1016/j.laa.2009.11.024 fatcat:7wfllld5qnbrbe4oyqbfpyvv5a