Perturbation bound of the Drazin inverse

摘要

A perturbation theory for the Drazin inverse AD is developed. This theory is based on the Jordan canonical form of A. Norm estimates of ∥(A+E)#−AD∥ are derived when AD and A+E are of the same rank and ∥E∥ is small. A hard problem by Campbell and Meyer [Linear Algebra Appl. 10 (1975) 77–83] is partially solved.