Sangwine, Stephen J and Hitzer, Eckhard (2020) Polar decomposition of complexified quaternions and octonions. Advances in Applied Clifford Algebras, 30 (2). DOI https://doi.org/10.1007/s00006-020-1048-y
Sangwine, Stephen J and Hitzer, Eckhard (2020) Polar decomposition of complexified quaternions and octonions. Advances in Applied Clifford Algebras, 30 (2). DOI https://doi.org/10.1007/s00006-020-1048-y
Sangwine, Stephen J and Hitzer, Eckhard (2020) Polar decomposition of complexified quaternions and octonions. Advances in Applied Clifford Algebras, 30 (2). DOI https://doi.org/10.1007/s00006-020-1048-y
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 Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 21 Feb 2020 13:53 |
| Last Modified: | 06 Jan 2022 14:11 |
| URI: | http://repository.essex.ac.uk/id/eprint/26873 |
Available files
Filename: CES-535-post-peer-review.pdf