| 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 |
|
| 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 |
|
