Perturbed spectra of defective matrices. Issue 3 (5th March 2003)

• Record Type: Journal Article
• Authors: Konstantinov, Mihail; Mehrmann, Volker; Petkov, Petko
• Is Part Of: Journal of applied mathematics. Volume 2003:Issue 3(2003)
• Page Start: 115
• Page End: 140
• Publication Date: 2003-03-05
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/S1110757X0320512X
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrixA is changed toA + t E, whereE ≠ 0 andt > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrixE 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.