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Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions

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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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Authors and Affiliations

  1. School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom

    Stephen J. Sangwine

  2. 5620 Oak View Court, Savage, MN, 55378-4695, USA

    Todd A. Ell

  3. GIPSA-Lab, Département Images et Signal, Domaine Universitaire, 961 Rue de la Houille Blanche, BP 46, 38402, Saint Martin d’Hères cedex, France

    Nicolas Le Bihan

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  1. Stephen J. Sangwine
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  2. Todd A. Ell
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  3. Nicolas Le Bihan
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Correspondence to Stephen J. Sangwine.

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Sangwine, S.J., Ell, T.A. & Le Bihan, N. Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions. Adv. Appl. Clifford Algebras 21, 607–636 (2011). https://doi.org/10.1007/s00006-010-0263-3

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  • DOI: https://doi.org/10.1007/s00006-010-0263-3

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