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The Relation Between the Companion Matrix and the Companion Polynomial in \(\mathbb {R}^4\) Algebras

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Abstract

We prove that the quaternionic companion polynomial is identical with the characteristic polynomial of the complex matrix which is obtained by isomorphism from the quaternionic companion matrix. And we show that this is also true for the other three noncommutative algebras in \(\mathbb {R}^4\) which include the coquaternions.

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Authors and Affiliations

  1. Department of Mathematics, University of Chemistry and Technology, Prague, Technická 5, 166 28, Prague 6, Czech Republic

    Drahoslava Janovská

  2. Faculty on Mathematics, Informatics, and Natural Sciences (MIN), University of Hamburg, Bundestraße 55, 20146, Hamburg, Germany

    Gerhard Opfer

Authors
  1. Drahoslava Janovská
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  2. Gerhard Opfer
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Correspondence to Gerhard Opfer.

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Communicated by Rafał Abłamowicz

Dedicated to the memory of Ivo Marek (1933–2017).

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Janovská, D., Opfer, G. The Relation Between the Companion Matrix and the Companion Polynomial in \(\mathbb {R}^4\) Algebras. Adv. Appl. Clifford Algebras 28, 76 (2018). https://doi.org/10.1007/s00006-018-0892-5

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  • DOI: https://doi.org/10.1007/s00006-018-0892-5

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