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 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 va...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X0320512X |
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| _version_ | 1832561963469635584 |
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| author | Mihail Konstantinov Volker Mehrmann Petko Petkov |
| author_facet | Mihail Konstantinov Volker Mehrmann Petko Petkov |
| author_sort | Mihail Konstantinov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-245a618f1e5c44a6b3cdb989275e8899 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-245a618f1e5c44a6b3cdb989275e88992025-02-03T01:23:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-012003311514010.1155/S1110757X0320512XPerturbed spectra of defective matricesMihail Konstantinov0Volker Mehrmann1Petko Petkov2Department of Automatics, University of Architecture and Civil Engineering, 1 Christo Smirnenski Blvd., Sofia 1046, BulgariaInstitut für Mathematik, MA 4–5, Technische Universitfät Berlin, Strasse des 17.Juni 136, Berlin D-10623, GermanyDepartment of Systems and Control, Faculty of Automatics, Technical University of Sofia, Sofia 1756, BulgariaThis 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.http://dx.doi.org/10.1155/S1110757X0320512X |
| spellingShingle | Mihail Konstantinov Volker Mehrmann Petko Petkov Perturbed spectra of defective matrices Journal of Applied Mathematics |
| title | Perturbed spectra of defective matrices |
| title_full | Perturbed spectra of defective matrices |
| title_fullStr | Perturbed spectra of defective matrices |
| title_full_unstemmed | Perturbed spectra of defective matrices |
| title_short | Perturbed spectra of defective matrices |
| title_sort | perturbed spectra of defective matrices |
| url | http://dx.doi.org/10.1155/S1110757X0320512X |
| work_keys_str_mv | AT mihailkonstantinov perturbedspectraofdefectivematrices AT volkermehrmann perturbedspectraofdefectivematrices AT petkopetkov perturbedspectraofdefectivematrices |