Mihail Konstantinov, Volker Mehrmann, Petko Petkov, "Perturbed spectra of defective matrices", Journal of Applied Mathematics, vol. 2003, Article ID 971396, 26 pages, 2003. https://doi.org/10.1155/S1110757X0320512X
Perturbed spectra of defective matrices
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.
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