Perturbed spectra of defective matrices. Issue 3 (5th March 2003) - Konstantinov, Mihail; Mehrmann, Volker; Petkov, Petko
Abstract : This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrixA is changed toA + t E, whereE ≠ 0 andt > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrixE varies over the sphere‖ E ‖   = ρ > 0 . We partially characterize the leading exponents noting that the description of the set of all leading exponents remains an open problem.