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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Jeffrey Uhlmann, Department of Electrical Engineering and Computer Science, University of Missouri, Columbia, USA
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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.
Algebras, Complex Numbers, Convolutions, Hypercomplex Algebras, Mathematics Education, Vector Spaces
To cite this article
A Matrix-Vector Construction of the Algebra of Complex Numbers, Applied and Computational Mathematics.
Vol. 8, No. 1,
2019, pp. 1-2.
Copyright © 2019 Authors retain the copyright of this article.
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Lars Ahlfors, Complex Analysis (3rd ed.), McGraw-Hill, 1979.
J. Hadamard, “Resolution d’une question relative aux determinants,” Bulletin des Sciences Mathematiques Series, 2 (17), pp. 240-246, 1893.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1990.
W. Hamilton, ed., Elements of Quaternions, London (UK), 1866.
I. L. Kantor and A. S. Solodvnikov, Hypercomplex Numbers: An Elementary Introduction to Algebras, New York: Springer-Verlag, 1989.