混合型交换四元数矩阵的指数形式  

On exponential of hybrid commutative quaternion matrix

作　　者：孔祥强 KONG Xiangqiang(School of Mathematics and Statistics, Heze University, Heze 274015, China)

机构地区：[1]菏泽学院数学与统计学院,山东菏泽274015

出　　处：《安徽大学学报（自然科学版）》2021年第1期7-13,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11871302);山东省自然科学基金资助项目(ZR201709250116,ZR2017MA029);菏泽学院科研基金科技计划项目(XY17KJ02);菏泽学院大学数学课程“线上”+“线下”混合式教学模式研究与实践项目(2018311)。

摘　　要：通过引入混合型交换四元数的复表示,将对混合型交换四元数的研究转化为对复数域上矩阵的研究.首先,给出混合型交换四元数矩阵复表示的性质;其次,依托矩阵的复表示,得到混合型交换四元数矩阵指数形式的系列定理,给出求指数形式的新方法;最后,利用数值算例给出求混合型交换四元数矩阵指数形式的具体过程.In the paper,by introducing the complex representation of hybrid commutative quaternion,the study of hybrid commutative quaternion was transformed into the study of matrix in complex field.Firstly,the properties of complex representation of hybrid commutative quaternion matrix were given.Secondly,a series of theorems for the exponential form of hybrid commutative quaternion matrix were obtained based on the complex representation of matrix,and a new method for solving exponential form was given.Finally,some numerical examples were given to illustrate the process of solving exponential form of hybrid commutative quaternion matrix.

关 键 词：混合型交换四元数 交换四元数矩阵 指数形式 复表示 

分 类 号：O153[理学—基础数学]