## Journal of Applied Mathematics

### Perturbed spectra of defective matrices

#### 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 $E\neq 0$ 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 $\|E\| = \rho > 0$. 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

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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