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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 B C D ) (A and D are square matrices) with generalized Schur complement is zero.

Generalizations of some conditions for Drazin inverses of the sum of two matrices