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Cyclic matrices and polynomial interpolation over division rings.
- Source :
-
Linear Algebra & its Applications . Aug2022, Vol. 646, p132-174. 43p. - Publication Year :
- 2022
-
Abstract
- As is well known, any complex cyclic matrix A is similar to the unique companion matrix associated with the minimal polynomial of A. On the other hand, a cyclic matrix over a division ring F is similar to a companion matrix of a polynomial which is defined up to polynomial similarity. In this paper we study more rigid canonical forms by embedding a given cyclic matrix over a division ring F into a controllable or an observable pair. Using the characterization of ideals in F [ z ] in terms of controllable and observable pairs we consider ideal interpolation schemes in F [ z ] which merge into polynomial interpolation problems containing both left and right interpolation conditions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 646
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 156552518
- Full Text :
- https://doi.org/10.1016/j.laa.2022.03.030