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On the Quaternionic Quadratic Equation \(\varvec{xax+bx+xc+d=0}\)

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A Correction to this article was published on 11 September 2020

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Abstract

It is shown that the roots of the quaternion quadratic equation \(xax+bx+xc+d=0\) can be found by computing the eigenvalues of a companion matrix. This allows to completely discuss the number of solutions and to apply some Geršgorin type theorems. Another consequence is the possibility of constructing equations with a given number of solutions.

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  • 11 September 2020

    Unfortunately, the author names in the reference 9 was wrongly published in the original article and the reference should be

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Acknowledgements

We thank two anonymous reviewers for several helpful comments.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    E. Macías-Virgós

  2. Facultade de Economía e Empresa, Universidade da Coruña, 15071, A Coruña, Spain

    M. J. Pereira-Sáez

Authors
  1. E. Macías-Virgós
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  2. M. J. Pereira-Sáez
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Correspondence to E. Macías-Virgós.

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This work was partially supported by MTM2016-78647-P research project from MINECO-Spain and FEDER. The first author was also supported by Xunta de Galicia 2015-PG006.

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Macías-Virgós, E., Pereira-Sáez, M.J. On the Quaternionic Quadratic Equation \(\varvec{xax+bx+xc+d=0}\). Adv. Appl. Clifford Algebras 29, 81 (2019). https://doi.org/10.1007/s00006-019-0999-3

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  • DOI: https://doi.org/10.1007/s00006-019-0999-3

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