四元数体上共轭辛矩阵的结构及应用  

The Structure of Conjugate Symplectic Matrix over Quaternion Field and Its Applications

作　　者：黄敬频 沈聪 陈丽蔓 陆云双 

机构地区：[1]广西民族大学理学院,广西南宁530006 [2]广西混杂计算与集成电路设计分析重点实验室,广西南宁530006

出　　处：《数学的实践与认识》2017年第24期259-264,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661011);广西混杂计算重点实验室开放基金项目(HCIC201504);广西民族大学研究生创新项目(gxun-chxzs2016127)

摘　　要：把实数域上的辛矩阵概念推广到四元数体上形成共轭辛矩阵类.用矩阵四分块形式刻划了正定辛矩阵和自共轭辛矩阵的特征结构.作为应用,给出四元数矩阵方程AS=B存在四分块对角型共轭辛矩阵解的充要条件及其解的表达式,同时用数值算例说明所给方法的可行性.In this paper, the conjugate symplectic matrix over quaternion field is defined,which the concept of real symplectic matrix is generalized. It is depicted eigenstructure of the positive definite and self-conjugate symplectic matrix by four block matrix respectively.As application, sufficient and necessary conditions for existence and uniqueness of solution with block diagonal conjugate symplectic matrix for the quaternion matrix equation AS = B and the expression of its solution are obtained, meanwhile the feasibility of this method is illustrated by using one example.

关 键 词：四元数体 共轭辛矩阵 结构 应用 

分 类 号：O151.21[理学—数学]