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Perturbed spectra of defective matrices

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  • Mihail Konstantinov
  • Volker Mehrmann
  • Petko Petkov

Abstract

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 + t E , 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.

Suggested Citation

  • Mihail Konstantinov & Volker Mehrmann & Petko Petkov, 2003. "Perturbed spectra of defective matrices," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-26, January.
    • Handle: RePEc:hin:jnljam:971396
    DOI: 10.1155/S1110757X0320512X
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