Dual Quaternion Involutions and Anti-Involutions |
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Authors: | Murat Bekar Yusuf Yayı |
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Institution: | 1. Department of Mathematics and Computer Sciences, Konya Necmettin Erbakan University, 42090, Konya, Turkey 2. Department of Mathematics, Ankara University, 06100, Ankara, Turkey
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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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