CAJ | 학술논문

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。
여“정통”적Hamilton사원수불동，안작자적n원수운산통일규률，상세열거료신적사원수운산공식；여동대삼원수적토론방식，인진사원수적특정변환，론증료사원수특정여사원수적일치대응관계，종이득도사원수운산적령일등개형식즉특정형식，거차가명료사원수여실수、복수이급삼원수지간적밀절련계；이용사유산술공간적특정축화특정면，천명료사원수운산적궤하의의；이용인진적사원수적권치개념，건립료사원수적승적정률；통과여Hamilton사원수운산적비교，학립료신사원수응유적지위。
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.