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Polar decomposition of complexified quaternions and octonions

Sangwine, Stephen J and Hitzer, Eckhard (2020) 'Polar decomposition of complexified quaternions and octonions.' Advances in Applied Clifford Algebras. ISSN 0188-7009

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Abstract

We present a hitherto unknown polar representation of complexified quaternions (also known as biquaternions), also applicable to complexified octonions. The complexified quaternion is factored into the product of two exponentials, one trigonometric or circular, and one hyperbolic. The trigonometric exponential is a real quaternion, the hyperbolic exponential has a real scalar part and imaginary vector part. This factorisation is shown to be isomorphic to the polar decomposition of linear algebra.

Item Type: Article
Uncontrolled Keywords: biquaternion, quaternion, polar decomposition
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Elements
Date Deposited: 21 Feb 2020 13:53
Last Modified: 24 Feb 2020 15:15
URI: http://repository.essex.ac.uk/id/eprint/26873

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