Reachability matrices and cyclic matrices
Please always quote using this URN: urn:nbn:de:bvb:20-opus-68074
- We study reachability matrices R(A, b) = [b,Ab, . . . ,An−1b], where A is an n × n matrix over a field K and b is in Kn. We characterize those matrices that are reachability matrices for some pair (A, b). In the case of a cyclic matrix A and an n-vector of indeterminates x, we derive a factorization of the polynomial det(R(A, x)).
| Author: | Augusto Ferrante, Harald K. Wimmer |
|---|---|
| URN: | urn:nbn:de:bvb:20-opus-68074 |
| Document Type: | Journal article |
| Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
| Language: | English |
| Year of Completion: | 2010 |
| Source: | In: Electronic Journal of Linear Algebra (2010) 20, 95-102. |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| GND Keyword: | Mathematik |
| Tag: | Hautus test; Krylow matrix; Reachability matrix; Vandermonde matrix; companion matrix; cyclic matrix; nonderogatory matrix |
| Release Date: | 2012/10/04 |
| Note: | AMS subject classifications. 15A03, 15A15, 93B05 |
| Licence (German): |  CC BY-NC-SA: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell, Weitergabe unter gleichen Bedingungen |