Title |
Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras / |
Authors |
Dargys, Adolfas ; Acus, Artūras |
DOI |
10.15388/namc.2022.27.29528 |
Full Text |
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Is Part of |
Nonlinear analysis: modelling and control.. Vilnius : Vilniaus universiteto leidykla. 2022, vol. 27, no. 6, p. 1129-1149.. ISSN 1392-5113. eISSN 2335-8963 |
Keywords [eng] |
Clifford (geometric) algebra ; exponential and logarithm of Clifford numbers ; quaternions |
Abstract [eng] |
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. |
Published |
Vilnius : Vilniaus universiteto leidykla |
Type |
Journal article |
Language |
English |
Publication date |
2022 |
CC license |
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