The Explicit Expression of the Drazin Inverse and Its Application

Abstract

We give explicit expressions of ${(P\pm Q)}_d$ of two matrices $P$ and $Q$, in terms of $P$, $Q$, $P_d$, and $Q_d$, ${(P\pm I)}_d$, under the condition that $PQ=P$, and apply the result to finding an explicit representation for the Drazin inverse of some $2\times 2$ block matrix.