generalizations of some conditions for Drazin inverses of the sum of two matrices
Abstract
In this article, we present some formulas of the Drazin inverses of the sum of two
matrices under the conditions P2QP = 0; P2Q2 = 0, QPQ = 0 and PQP2 = 0;
PQ2 = 0, QP3 = 0 respectively. These conditions are weaker than those used
in some literature on this subject. Furthermore, we apply our results to give
the representations for the Drazin inverses of block matrix
(A and
D are square matrices) with generalized Schur complement is zero.
matrices under the conditions P2QP = 0; P2Q2 = 0, QPQ = 0 and PQP2 = 0;
PQ2 = 0, QP3 = 0 respectively. These conditions are weaker than those used
in some literature on this subject. Furthermore, we apply our results to give
the representations for the Drazin inverses of block matrix
(A and
D are square matrices) with generalized Schur complement is zero.
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