Perturbed spectra of defective matrices
Μ.Μ. Konstantinov, Volker Mehrmann, Petko H. Petkov · Journal of Applied Mathematics · 2003
This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A + tE, where E ≠ 0 and t > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrix E 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.