Some results for the Drazin inverses of the sum of two matrices and some block matrices
Summary: We give a formula of \((P+Q)^D\) under the conditions \(P^2+QPQ=0\), \(P^3Q=0\), and \(PQPQ=0\). Then, we apply it to give some expressions for the Drazin inverse of block matrix \(M=\begin{pmatrix} A&B\\C&D\end{pmatrix}\) (\(A\) and \(D\) are square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examples are given to illustrate our results.
scientific article; zbMATH DE number 6950883