Journal of Applied Mathematics
Volume 2003 (2003), Issue 3, Pages 115-140
Perturbed spectra of defective matrices
1Department of Automatics, University of Architecture and Civil Engineering, 1 Christo Smirnenski Blvd., Sofia 1046, Bulgaria
2Institut für Mathematik, MA 4–5, Technische Universitfät Berlin, Strasse des 17.Juni 136, Berlin D-10623, Germany
3Department of Systems and Control, Faculty of Automatics, Technical University of Sofia, Sofia 1756, Bulgaria
Received 22 May 2002; Revised 7 October 2002
Copyright © 2003 Mihail Konstantinov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is devoted to the perturbation theory for defective
matrices. We consider the asymptotic expansions of the perturbed
spectrum when a matrix is changed to , where and
is a small parameter. In particular, we analyse the rational
exponents that may occur when the matrix varies over the sphere
. We partially characterize the leading exponents
noting that the description of the set of all leading exponents
remains an open problem.