A Note on Representations of the Drazin Inverse for Complex Partitioned Matrices

In this paper, we present explicit representations for Drazin inverses of the sum P+Q under the conditions P2Q=0, Q2PQ=0, and Q(PQ)2=0. Then, we apply our results to derive a series of representations for the Drazin inverses of a 2×2 complex partitioned matrix ABCD, where A and D are square complex matrices. Numerical examples are provided to show that the assumptions used here are genuinely weaker than those in a number of earlier results.