Fundamental representations and algebraic properties of biquaternions or complexified quaternions

Stephen Sangwine (1) , Todd Ell , Nicolas Le Bihan (2)

1 University of Essex
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

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

Domaines: Recherche d'information [cs.IR]

Stephen Sangwine, Todd Ell, Nicolas Le Bihan. Fundamental representations and algebraic properties of biquaternions or complexified quaternions. Advances in Applied Clifford Algebras, 2011, 21 (3), pp.607-636. ⟨10.1007/s00006-010-0263-3⟩. ⟨hal-00788240⟩