Perturbed spectra of defective matrices
- Resource Type
- article
- Authors
- Mihail Konstantinov; Volker Mehrmann; Petko Petkov
- Source
- Journal of Applied Mathematics, Vol 2003, Iss 3, Pp 115-140 (2003)
- Subject
- Mathematics
QA1-939
- Language
- English
- ISSN
- 1110-757X
1687-0042
1110757X
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.