Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras

Author:

Dargys Adolfas,Acus ArtūrasORCID

Abstract

The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra. Closed form expressions for a multivector exponential and logarithm are presented in real geometric algebras Clp;q when n = p + q = 1 (complex and hyperbolic numbers) and n = 2 (Hamilton, split, and conectorine quaternions). Starting from Cl0;1 and Cl1;0 algebras wherein square of a basis vector is either –1 or +1, we have generalized exponential and logarithm formulas to 2D quaternionic algebras Cl0;2, Cl1;1, and Cl2;0. The sectors in the multivector coefficient space, where 2D logarithm exists are found. They are related with a square root of the multivector.

Publisher

Vilnius University Press

Subject

Applied Mathematics,Analysis

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Generalized relativistic transformations in Clifford spaces and their physical implications;International Journal of Geometric Methods in Modern Physics;2024-02-09

2. Logarithm of multivector in real 3D Clifford algebras;Nonlinear Analysis: Modelling and Control;2023-11-07

3. Survey of new applications of geometric algebra;Mathematical Methods in the Applied Sciences;2023-07-31

4. The characteristic polynomial in calculation of exponential and elementary functions in Clifford algebras;Mathematical Methods in the Applied Sciences;2023-07-11

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