Some representations for the Drazin inverse of a modified matrix

In this paper, we give some results for the Drazin inverse of a modified matrix $$M=A-CD^dB$$ M = A - C D d B with the generalized Schur complement $$Z=D-BA^dC$$ Z = D - B A d C under some conditions. Further, we present some new results for the Drazin inverse of the modified matrix $$M=A-CD^dB$$ M = A - C D d B , when the generalized Schur complement $$Z=0$$ Z = 0 under some conditions. As a result, some conclusions are obtained directly from our results.