三对角矩阵加箭形矩阵约束四元数矩阵方程AXA^*=B问题研究  

Research on Quaternion Matrix Equation AXA^*=B with Tridiagonal-plus-Arrow Matrices Constraints

作　　者：吴恒飞 张宗标 WU Heng-fei;ZHANG Zong-biao(Department of Electronic and Information Engineering,Bozhou College,Bozhou 236800,Anhui,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800

出　　处：《韶关学院学报》2020年第9期7-12,共6页Journal of Shaoguan University

基　　金：安徽省高校自然科学研究项目(KJ2017A704);亳州学院科研项目(bsky201430);亳州学院教研项目(2017ybjy22).

摘　　要：运用四元数矩阵实表示,融合三对角加箭形矩阵的特殊结构,利用矩阵的拉直算法与Kronecker积,把四元数矩阵方程AXA^*=B转换成无约束的实矩阵方程,给出该方程具有三对角加箭形和自共轭三对角加箭形矩阵解的充要条件及通解表达式.最后,在对应解集中,求得事先给出的四元数三对角加箭形矩阵的极小Frobenius范数最佳逼近解.By using the real representation quaternion matrix,the special structure of tridiagonal-plus-arrow matrices,the matrix straightening algorithm and Kronecker product,the quaternion matrix equation AXA^*=B can be transformed into an unconstrained real matrix equation.Then the necessary and sufficient conditions for the existence of a tridiagonal matrix plus arrow matrices solution and a self-conjugate tridiagonal matrix plus arrow matrices solution of the equation are obtained.Finally,in the corresponding solution set,the optimal approximation solution is derived from a given quaternion tridiagonal-plus-arrow matrix equation with the least Frobenius norm.

关 键 词：四元数 矩阵实表示 KRONECKER积 自共轭解 最佳逼近 

分 类 号：O151.21[理学—数学]