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Cyclic matrices and polynomial interpolation over division rings
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NSTL
Elsevier
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.(c) 2022 Published by Elsevier Inc.
Cyclic matrixControllable and observable pairsMinimal polynomialCompanion matrixWEDDERBURN POLYNOMIALSVANDERMONDESIMILARITY
NSTL
Elsevier
