Journal of East China Normal University(Natural Science) >
De Moivre’s theorem for a matrix representation of hyperbolic split quaternions
Received date: 2021-01-22
Online published: 2022-11-22
In this paper, de Moivre’s theorem for a matrix representation of a class of hyperbolic split quaternions is studied. Firstly, the study of hyperbolic split quaternions is transformed into the study of a matrix representation of hyperbolic split quaternions. Secondly, by using the polar representation of a hyperbolic split quaternion, the three forms of de Moivre’s theorem for a matrix representation of the hyperbolic split quaternion are obtained, and Euler’s formula is extended. Thirdly, the root-finding formula of the hyperbolic split quaternion matrix representation equation is obtained. Finally, the validity of the conclusions is verified with some examples.
Xiangqiang KONG . De Moivre’s theorem for a matrix representation of hyperbolic split quaternions[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(6) : 8 -16 . DOI: 10.3969/j.issn.1000-5641.2022.06.002
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