An efficient method for solving equations in generalized quaternion and octonion algebras
Abstract
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of quaternions and the algebra of coquaternions. In this paper, we present the formulae to pass from a basis in the generalized quaternion algebras to a basis in the division quaternions algebra or to a basis in the coquaternions algebra and vice versa. The same result was obtained for the generalized octonion algebra. Moreover, we emphasize the applications of these results to the algebraic equations and De Moivre s formula in generalized quaternion algebras and in generalized octonion division algebras.
Cite
@article{arxiv.1405.5652,
title = {An efficient method for solving equations in generalized quaternion and octonion algebras},
author = {Cristina Flaut and Vitalii Shpakivskyi},
journal= {arXiv preprint arXiv:1405.5652},
year = {2014}
}
Comments
This paper will be joint with the paper arXiv:1405.5655 in a single article and resubmit to arxiv in this joint form