A Matrix-Vector Construction of the Algebra of Complex Numbers
Applied and Computational Mathematics
Volume 8, Issue 1, February 2019, Pages: 1-2
Received: Dec. 10, 2018; Accepted: Jan. 2, 2019; Published: Jan. 30, 2019
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Author
Jeffrey Uhlmann, Department of Electrical Engineering and Computer Science, University of Missouri, Columbia, USA
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Abstract
The aim of this paper is to describe an alternative way to think about the algebra of complex numbers that may be of pedagogical value for introducing related concepts such as linear transformations and convolutions. The method is to define a fixed linear transformation of complex numbers represented in vector form so that products can be evaluated elementwise in the transformed space. The principal results are concrete demonstrations that this can in fact be accomplished.
Keywords
Algebras, Complex Numbers, Convolutions, Hypercomplex Algebras, Mathematics Education, Vector Spaces
To cite this article
Jeffrey Uhlmann, A Matrix-Vector Construction of the Algebra of Complex Numbers, Applied and Computational Mathematics. Vol. 8, No. 1, 2019, pp. 1-2. doi: 10.11648/j.acm.20190801.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
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[2]
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R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1990.
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W. Hamilton, ed., Elements of Quaternions, London (UK), 1866.
[5]
I. L. Kantor and A. S. Solodvnikov, Hypercomplex Numbers: An Elementary Introduction to Algebras, New York: Springer-Verlag, 1989.
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