Further additive results on the Drazin inverse
Abstract
In this paper, we provide original representation for the Drazin inverse of $P+Q$ under the conditions $P^2Q=0$, $Q(PQ)^2=0$, $Q^2PQ^2=0$, $QPQ^3=0$ and $QPQ^2PQ=0$. Then, we apply our results to derive some new expressions for the Drazin inverse of a $2\times2$ complex block matrix $M=\begin{bmatrix}
A&B\\
C&D
\end{bmatrix}\in\mathbb{C}^{n\times n}$(where $A$ and $D$ are square matrices but not necessarily of the same size).
Finally, several illustrative numerical examples are given to demonstrate our results.
A&B\\
C&D
\end{bmatrix}\in\mathbb{C}^{n\times n}$(where $A$ and $D$ are square matrices but not necessarily of the same size).
Finally, several illustrative numerical examples are given to demonstrate our results.
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