Journal of Applied Mathematics

Perturbed spectra of defective matrices

Mihail Konstantinov, Volker Mehrmann, and Petko Petkov

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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+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.

Article information

Source
J. Appl. Math., Volume 2003, Number 3 (2003), 115-140.

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1049725733

Digital Object Identifier
doi:10.1155/S1110757X0320512X

Mathematical Reviews number (MathSciNet)
MR1982353

Zentralblatt MATH identifier
1039.15002

Subjects
Primary: 15A18: Eigenvalues, singular values, and eigenvectors 65F15

Citation

Konstantinov, Mihail; Mehrmann, Volker; Petkov, Petko. Perturbed spectra of defective matrices. J. Appl. Math. 2003 (2003), no. 3, 115--140. doi:10.1155/S1110757X0320512X. https://projecteuclid.org/euclid.jam/1049725733


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