HITZER, Eckhard
Senior Associate Professor Division of Arts and Sciences, College of Liberal Arts, International Christian University |
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Language | English |
Publication Date | 2019 |
Type | Technical Report, Preprint, etc. |
Title | Polar decomposition of complexified quaternions and octonions |
Contribution Type | Joint Work |
Journal | Technical Report, University of Essex, UK |
Journal Type | Another Country |
Publisher | University of Essex, UK |
Volume, Issue, Pages | (CES-535),pp.1-8 |
Responsible for | Part of text and computations. |
Author and coauthor | Stephen J. Sangwine, Eckhard Hitzer |
Details | We present a hitherto unknown polar representation of complexified quaternions (also known asbiquaternions), also applicable to complexified octonions. The complexified quaternion is factored intothe product of two exponentials, one trigonometric or circular, and one hyperbolic. The trigonometricexponential is a real quaternion, the hyperbolic exponential has a real scalar part and imaginary vectorpart. This factorisation is shown to be isomorphic to the polar decomposition of linear algebra. |