Hypercomplex Numbers and Roots of Algebraic Equation
- 1 January 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Journal of Geometry and Symmetry in Physics
- Vol. 64, 9-22
- https://doi.org/10.7546/jgsp-64-2022-9-22
Abstract
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 hyper -complex numbers are worthy of application in teaching and scientific research.Keywords
This publication has 4 references indexed in Scilit:
- A Note on the Representation of Clifford AlgebrasJournal of Geometry and Symmetry in Physics, 2021
- Stability Analysis of Quaternion-Valued Neural Networks: Decomposition and Direct ApproachesIEEE Transactions on Neural Networks and Learning Systems, 2017
- On Matrix Representations of Geometric (Clifford) AlgebrasJournal of Geometry and Symmetry in Physics, 2017
- Pairwise alignment of the DNA sequence using hypercomplex number representationBulletin of Mathematical Biology, 2004