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Polar decomposition of complexified quaternions and octonions

Sangwine, Stephen and Hitzer, Eckhard (2019) Polar decomposition of complexified quaternions and octonions. Technical Report. University of Essex, School of Computer Science and Electronic Engineering. (Unpublished)

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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: Monograph (Technical Report)
Uncontrolled Keywords: quaternion, octonion, polar decomposition
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Elements
Date Deposited: 24 Apr 2019 09:15
Last Modified: 24 Apr 2019 10:15
URI: http://repository.essex.ac.uk/id/eprint/24443

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