The perturbation theory for the Drazin inverse and its applications (Q1359186)

For an \(n\times n\) matrix \(A\), let \(A^D\) denote the Drazin inverse of \(A\). The main result of this paper is the following: If \(B=A+E\) where \(E=AA^DEAA^D\) and \(\delta=|A^DE|<1\), then \((|B^D- A^D|)/|A^D|\leq\delta/(1- \delta)\). An application to a perturbed linear system is given.