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.
| Published in | Applied and Computational Mathematics (Volume 8, Issue 1) |
| DOI | 10.11648/j.acm.20190801.11 |
| Page(s) | 1-2 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
Algebras, Complex Numbers, Convolutions, Hypercomplex Algebras, Mathematics Education, Vector Spaces
| [1] | Lars Ahlfors, Complex Analysis (3rd ed.), McGraw-Hill, 1979. |
| [2] | J. Hadamard, “Resolution d’une question relative aux determinants,” Bulletin des Sciences Mathematiques Series, 2 (17), pp. 240-246, 1893. |
| [3] | R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1990. |
| [4] | 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. |
APA Style
Jeffrey Uhlmann. (2019). A Matrix-Vector Construction of the Algebra of Complex Numbers. Applied and Computational Mathematics, 8(1), 1-2. https://doi.org/10.11648/j.acm.20190801.11
ACS Style
Jeffrey Uhlmann. A Matrix-Vector Construction of the Algebra of Complex Numbers. Appl. Comput. Math. 2019, 8(1), 1-2. doi: 10.11648/j.acm.20190801.11
AMA Style
Jeffrey Uhlmann. A Matrix-Vector Construction of the Algebra of Complex Numbers. Appl Comput Math. 2019;8(1):1-2. doi: 10.11648/j.acm.20190801.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.acm.20190801.11,
author = {Jeffrey Uhlmann},
title = {A Matrix-Vector Construction of the Algebra of Complex Numbers},
journal = {Applied and Computational Mathematics},
volume = {8},
number = {1},
pages = {1-2},
doi = {10.11648/j.acm.20190801.11},
url = {https://doi.org/10.11648/j.acm.20190801.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20190801.11},
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.},
year = {2019}
}
TY - JOUR T1 - A Matrix-Vector Construction of the Algebra of Complex Numbers AU - Jeffrey Uhlmann Y1 - 2019/01/30 PY - 2019 N1 - https://doi.org/10.11648/j.acm.20190801.11 DO - 10.11648/j.acm.20190801.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 2 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20190801.11 AB - 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. VL - 8 IS - 1 ER -
Email: