Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero
Let \(A^\pi\) denote the eigenprojection of a matrix \(A\) corresponding to the eigenvalue 0. The authors characterize matrices \(B\) such that \(B^\pi=A^\pi\), and derive from the results: (1) error bounds for the Drazin inverse of perturbation; (2) improvement of error bounds given by \textit{Y. Wei} [Appl. Math. Comput. 98, No. 1, 29-42 (1999; Zbl 0927.15004)], \textit{Y. Wei} and \textit{G. Wang} [Linear Algebra Appl. 258, 179-186 (1997; Zbl 0882.15003)], and \textit{N. Castro Gonzalez} and \textit{J. J. Koliha} [Integral Equations Oper. Theory 36, No. 1, 92-106 (2000; Zbl 0938.47009)], and (3) a new characterization of EP matrices.
scientific article; zbMATH DE number 1485565