论四元数体上广义埃尔米特矩阵的标准形

摘要

Three different real number representation over quaternion field,quaternion vector and matrix space are introduced. The calculation of quaternion field,quaternion vector and matrix are transformed into the one between vector and matrix over real number field. The obtained result can be transformed into quaternion field ,quaternion vector and matrix accurately. The calculation difficulty that the product can be not commutative over quaternion field can be overcome. By using algebraic constructive methods,the way that transforms symmetric matrix into standard form over number field has been generalized similarly to the one that transforms generalized Hermitian matrix into standard form over quaternion field.%在四元数与四元数向量、矩阵空间上引入三种不同的实数表示方式，将四元数之间及四元数向量与矩阵之间的运算化为实数域上向量与矩阵之间的运算，得到的计算结果可准确转换成四元数与四元数向量和矩阵，克服四元数之间因乘积不可交换而造成的运算困难，通过代数构造的方法把数域上的对称矩阵化标准形的方法类似地推广到四元数体上广义埃尔米特矩阵化标准形的方法。