2022 Hypercomplex Numbers and Roots of Algebraic Equation
Ying-Qiu Gu
J. Geom. Symmetry Phys. 64: 9-22 (2022). DOI: 10.7546/jgsp-64-2022-9-22


By means of hypercomplex numbers, in this paper we discuss algebraic equations and obtain some interesting relations. A structure equation$A^2=nA$ of a group is derived. The matrix representation of a group constitutes the basis elements of a hypercomplex number system. By a canonical real matrix representation of a cyclic group, we define the cyclic number system, which is exactly the solution space of the higher order algebraic equations, and thus can be used to solve the roots of algebraic equations. Hypercomplex numbers are linear algebras with definition of multiplication and division, satisfying the associativity and distributive law, which provide a unified, standard, and elegant language for many complex mathematical and physical objects. So, we have one more proof that the hypercomplex numbers are worthy of application in teaching and scientific research.


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Ying-Qiu Gu. "Hypercomplex Numbers and Roots of Algebraic Equation." J. Geom. Symmetry Phys. 64 9 - 22, 2022. https://doi.org/10.7546/jgsp-64-2022-9-22


Published: 2022
First available in Project Euclid: 13 December 2022

Digital Object Identifier: 10.7546/jgsp-64-2022-9-22

Rights: Copyright © 2022 Bulgarian Academy of Sciences, Institute of Mechanics


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