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

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.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