对偶分裂半四元数及其表示矩阵的棣莫弗定理OA
De Moivre's theorem of dual split semi-quaternions and its representation matrices
以对偶分裂半四元数的概念为依托,首先,基于对偶分裂半四元数不同的极表示形式,分别得到了 3种情形下的棣莫弗定理.其次,给出了对偶分裂半四元数的表示矩阵形式,将对偶分裂半四元数的研究转化为对其表示矩阵的研究,得到3种情形下对偶分裂半四元数表示矩阵的棣莫弗定理,并推广了欧拉公式.最后,通过算例验证了结论的正确性和有效性.
In this paper,relying on the concept of dual split semi-quaternions,firstly,based on the different polar representations of dual split semi-quaternions,the De Moivre's theorem was obtained in three cases,respectively.Secondly,the representations matrices of dual split semi-quaternions were given.The studies of dual split semi-quaternions were transformed into the study of its representation matrices,and the De Moivre's theorems for the representation matrices of dual split semi-quaternions were obtained in three cases,the Euler's formula was also extended.Finally,some examples were given to verify the correctness and validity of the conclusions.
孔祥强
菏泽学院数学与统计学院,山东菏泽 274015
数理科学
对偶分裂半四元数表示矩阵棣莫弗定理极表示
dual split semi-quaternionsrepresentation matricesDe Moivre's theorempolar representations
《安徽大学学报（自然科学版）》 2026 (3)
7-15,9
山东省自然科学基金资助项目(ZR201709250116)菏泽学院教学改革项目(JG202316)菏泽市社会科学规划课题(2025-ZZ-56)
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