On Complex Numbers in Higher Dimensions
Institute of Mathematics, University of Rostock, 18051 Rostock, Germany
Axioms 2022, 11(1), 22; https://doi.org/10.3390/axioms11010022
Submission received: 3 November 2021
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Revised: 23 December 2021
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Accepted: 28 December 2021
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Published: 7 January 2022
(This article belongs to the Special Issue Complex Analysis)
Abstract
The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is continued here in dimension four and above. To this end, the notions of geometric vector product and geometric exponential function are extended to arbitrary finite dimensions and some usual algebraic rules known from usual complex numbers are replaced with new ones. An application for the construction of directional probability distributions is presented.
Keywords:
geometric vector product; geometric vector power; geometric exponential function; vector division; spherical geometric coordinate product; spherical geometric coordinate vector ratio; multi-complex algebraic structure; multi-complex numbers; Euler-type representation; directional probability law
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MDPI and ACS Style
Richter, W.-D. On Complex Numbers in Higher Dimensions. Axioms 2022, 11, 22. https://doi.org/10.3390/axioms11010022
AMA Style
Richter W-D. On Complex Numbers in Higher Dimensions. Axioms. 2022; 11(1):22. https://doi.org/10.3390/axioms11010022
Chicago/Turabian StyleRichter, Wolf-Dieter. 2022. "On Complex Numbers in Higher Dimensions" Axioms 11, no. 1: 22. https://doi.org/10.3390/axioms11010022
APA StyleRichter, W.-D. (2022). On Complex Numbers in Higher Dimensions. Axioms, 11(1), 22. https://doi.org/10.3390/axioms11010022
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