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- W4308014733 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." @default.
- W4308014733 created "2022-11-07" @default.
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- W4308014733 date "2022-10-19" @default.
- W4308014733 modified "2023-10-14" @default.
- W4308014733 title "Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras" @default.
- W4308014733 doi "https://doi.org/10.15388/namc.2022.27.29528" @default.
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