On the Drazin Inverse of the Sum of Two Matrices

Abstract

We deduce the explicit expressions for ${(P+Q)}^D$ and ${\left(PQ\right)}^D$ of two matrices $P$ and $Q$ under the conditions $P^{2}Q=PQP$ and $Q^{2}P=QPQ$. Also, we give the upper bound of ${\left|\right|{(P+Q)}^D-P^D\left|\right|}_2$.