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Advances in Applied Clifford Algebras

, Volume 23, Issue 3, pp 657–671 | Cite as

Real Matrix Representations for the Complex Quaternions

Article

Abstract

Starting from known results, due to Y. Tian in [5], referring to the real matrix representations of the real quaternions, in this paper we will investigate the left and right real matrix representations for the complex quaternions and we will give some examples in the special case of the complex Fibonacci quaternions.

Keywords

Quaternion algebra complex Fibonacci quaternions matrix representation 

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References

  1. 1.
    Eilenberg S., Niven I.: The “ fundamental theorem of algebra” for quaternions. Bull. Amer. Math. Soc. 50, 246–248 (1944)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    S. Halici, On complex Fibonacci Quaternions. Adv. in Appl. Clifford Algebras, doi: 10.1007/s00006-012-0337-5.
  3. 3.
    Horadam A. F.: Complex Fibonacci Numbers and Fibonacci Quaternions. Amer. Math. Monthly 70, 289–291 (1963)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    W.D.Smith, Quaternions, octonions, and now, 16–ons, and 2n–ons; New kinds of numbers. www.math.temple.edu/wds/homepage/nce2.ps, 2004.
  5. 5.
    Y. Tian, Matrix reprezentations of octonions and their applications. Adv. in Appl. Clifford Algebras 10 (1) (2000), 61–90.Google Scholar
  6. 6.
    Y. Tian, Matrix Theory over the Complex Quaternion Algebra. arXiv:math/0004005v1, 1 April 2000.Google Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceOvidius UniversityConstantaRomania
  2. 2.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Sciences of UkraineKiev-4Ukraine

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