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Dual Quaternion Involutions and Anti-Involutions

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Abstract

An involution or anti-involution is a self-inverse linear mapping. In this paper, we present involutions and anti-involutions of dual quaternions. In order to do this, quaternion conjugate, dual conjugate and total conjugate are defined for a dual quaternion and these conjugates are used in some transformations in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion and dual quaternion involutions and anti-involutions are given.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Konya Necmettin Erbakan University, 42090, Konya, Turkey

    Murat Bekar

  2. Department of Mathematics, Ankara University, 06100, Ankara, Turkey

    Yusuf Yayı

Authors
  1. Murat Bekar
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  2. Yusuf Yayı
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Correspondence to Murat Bekar.

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Bekar, M., Yayı, Y. Dual Quaternion Involutions and Anti-Involutions. Adv. Appl. Clifford Algebras 23, 577–592 (2013). https://doi.org/10.1007/s00006-013-0398-0

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  • DOI: https://doi.org/10.1007/s00006-013-0398-0

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