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Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions |
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| Authors: | Stephen J Sangwine Todd A Ell Nicolas Le Bihan |
| Institution: | 1. School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom 2. 5620 Oak View Court, Savage, MN, 55378-4695, USA 3. GIPSA-Lab, Département Images et Signal, Domaine Universitaire, 961 Rue de la Houille Blanche, BP 46, 38402, Saint Martin d’Hères cedex, France |
| Abstract: | The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms, polar forms, and inner products. The notation is consistent throughout, even between representations, providing a clear account of the many ways in which the component parts of a biquaternion may be manipulated algebraically. |
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