对偶分裂四元数的表示矩阵的棣莫弗定理

De Moivre s theorem for representation matrix of dual split quaternions

以对偶分裂四元数的表示矩阵为基础,利用对偶分裂四元数的极表示,得到了对偶分裂四元数表示矩阵的3种形式的棣莫弗定理,并推广了欧拉公式.给出了表示矩阵方程的求根公式.利用数值算例验证了所得结论的正确性.

In this paper,based on the representation matrix of dual split quaternions,firstly,by using the polar representation of dual split quaternions,the three forms of De Moivre s theorem for representation matrix of dual split quaternions are obtained,and Euler s formula is extended.Secondly,the formula for finding the roots of the representation matrix equation is given.Finally,numerical examples are used to verify the correctness of the conclusions.