Quaternion Involutions

Details Quaternion Involutions Quaternion Involutions

2005-06-02

arxiv.org/abs/math/0506034v1

Computers and Mathematics with Applications, 53, (1), January 2007, 137-143

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.camwa.2006.10.029

An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of involutions. We show that the conjugate of a quaternion may be expressed using three mutually perpendicular involutions. We also show that any set of three mutually perpendicular quaternion involutions is closed under composition. Finally, we show that projection of a vector or quaternion can be expressed concisely using involutions.

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