论四元数体上广义埃尔米特矩阵的标准形  

On the Standard Form of Generalized Hermitian Matrix over Quaternion Field

作　　者：杨衍婷[1] 

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000

出　　处：《河南科学》2015年第7期1076-1080,共5页Henan Science

基　　金：咸阳师范学院专项科研基金项目(13XSYK007)

摘　　要：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.Three different real number representation over quaternion field,quaternion vector and matrix space areintroduced. The calculation of quaternion field,quaternion vector and matrix are transformed into the one betweenvector and matrix over real number field. The obtained result can be transformed into quaternion field,quaternionvector and matrix accurately. The calculation difficulty that the product can be not commutative over quaternion fieldcan be overcome. By using algebraic constructive methods,the way that transforms symmetric matrix into standardform over number field has been generalized similarly to the one that transforms generalized Hermitian matrix intostandard form over quaternion field.

关 键 词：四元数体 分量矩阵 广义埃尔米特矩阵 标准形 

分 类 号：O151[理学—数学]