THE DRAZIN INVERSES OF THE SUM OF TWO MATRICES AND BLOCK MATRIX

In this paper, we give a formula of (P +Q)D under the condi- tions P2Q +QPQ = 0 and P3Q = 0: Then applying it to give some results of block matrix M = ( A B C D ) (A and D are square matrices) with gener- alized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.