Ell, Todd A and Sangwine, Stephen J (2007) Quaternion involutions and anti-involutions. Computers & Mathematics with Applications, 53 (1). pp. 137-143. DOI https://doi.org/10.1016/j.camwa.2006.10.029
Ell, Todd A and Sangwine, Stephen J (2007) Quaternion involutions and anti-involutions. Computers & Mathematics with Applications, 53 (1). pp. 137-143. DOI https://doi.org/10.1016/j.camwa.2006.10.029
Ell, Todd A and Sangwine, Stephen J (2007) Quaternion involutions and anti-involutions. Computers & Mathematics with Applications, 53 (1). pp. 137-143. DOI https://doi.org/10.1016/j.camwa.2006.10.029
Abstract
An involution or anti-involution is a self-inverse linear mapping. In this paper we study quaternion involutions and anti-involutions. We review formal axioms for such involutions and anti-involutions. We present two mappings, one a quaternion involution and one an anti-involution, and a geometric interpretation of each as reflections. We present results on the composition of these mappings and show that the quaternion conjugate may be expressed using three mutually perpendicular anti-involutions. Finally, we show that projection of a vector or quaternion can be expressed concisely using three mutually perpendicular anti-involutions. © 2007 Elsevier Ltd. All rights reserved.
Item Type: | Article |
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Uncontrolled Keywords: | quaternion; involution; anti-involution |
Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 28 Mar 2013 15:28 |
Last Modified: | 07 Aug 2024 19:51 |
URI: | http://repository.essex.ac.uk/id/eprint/5949 |