中文摘要：

本文在Q（P＋Q）Q（P＋Q）=0,P2 Q=QPQ2=0的条件下,给出两个矩阵和的Drazin逆（P＋Q）D的表达式.同时,应用此结果,得到四分块矩阵的Drazin逆的表示,并给出数值算例,说明其正确性及有效性.

英文摘要：

In this paper,we show the formula of the Drazin inverse of P＋Q under the conditions of Q（P＋Q）Q（P＋Q）=0,P2 Q=QPQ2=0.At the same time,we apply this result to gain the Drazin inverse of the block matrix.What＇s more,we list numerical example of 2×2block matrix to illustrate its correctness and effectiveness.