【摘要】 与“正统”的 Hamilton四元数不同 ,按作者的 n元数运算统一规律 ,详细列举了新的四元数运算公式 ;如同对三元数的讨论方式 ,引进四元数的特征变换 ,论证了四元数特征与四元数的一致对应关系 ,从而得到四元数运算的另一等价形式即特征形式 ,据此可明了四元数与实数、复数以及三元数之间的密切联系 ;利用四维算术空间的特征轴和特征面 ,阐明了四元数运算的几何意义 ;利用引进的四元数的权值概念 ,建立了四元数的乘积定律 ;通过与 Hamilton四元数运算的比较 ,确立了新四元数应有的地位更多还原

【Abstract】 The new four ary number, is different with the orthodox ideas of Hamilton’s quarternions.According to the writers’ unified pattern of operation on n ary number,the formulas of operation for four ary number are listed in detailed. Like the way discussed for three ary number, it introduced the characteristic transfermation to four ary number,and proved the identical corresponding relationship between four ary number and its characteristic,and get out another equal form of operation for four ary number,i.e. the characteristic form. On it,the close connection among four ary number with real number, complex number and three ary number may be going clear.Use the characteristic axis and the characteristic plane of four dimention arithmetic space, the geometric meaning of the operation of four ary number is described clearly. Using the concept of weight value is introduced,set up the new ideas of product law of four ary number.Through comparing on operation of four ary number with Hamilton’s quarternions,it established the position that new four ary number ought to have.更多还原