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Type: Journal article
Title: Functions of multivector variables
Author: Chappell, J.
Iqbal, A.
Gunn, L.
Abbott, D.
Citation: PLoS One, 2015; 10(3):e0116943-1-e0116943-21
Publisher: Public Library of Science
Issue Date: 2015
ISSN: 1932-6203
Statement of
James M. Chappell, Azhar Iqbal, Lachlan J. Gunn, Derek Abbott
Abstract: As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that provides a particularly versatile algebraic framework.
Keywords: Mathematics; Algorithms
Rights: © 2015 Chappell et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
RMID: 0030025267
DOI: 10.1371/journal.pone.0116943
Appears in Collections:Electrical and Electronic Engineering publications

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