改进四元数的共轭

Conjugate of Improved Quaternions

共轭与对称是复数系重要的运算,四元数的引入将实数域扩充到复数域,并用复数来表示平面向量.改进四元数的共轭与对称是对其进一步研究与应用的不可回避的环节之一,所以提出改进四元数共轭的定义并证明其性质,证明改进四元数是符合数系扩展原则的一种超复数.作为数学工具,其在机构学等其他领域的应用会更为广泛.

Conjugate and symmetry are important operations of complex numbers. The introduc- tion of quaternion has extended real numbers to complex numbers, which can be used to represent plane vectors. It is one of the inevitable links to improve the conjugate and symmetry of quaterni- ons in further researches and applications of this field. In this paper we first defined the conjugate of quaternions, and then we proved its nature, holding that the improved quaternion is a hyper- complex which corresponds to the numerical-system expansion principle. As a mathematical tool, it has a wider application in such fields as mechanism studies.