爪形矩阵约束四元数矩阵方程AXB=C的求解  

Solution of Quaternion Matrix Equation AXB = C with Paw Form Matrix Constraints

作　　者：吴恒飞 张宗标 WU Hengfei;ZHANG Zongbiao(Department of Electronic and Information Engineering,Bozhou University,Bozhou,Anhui 236800,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：《西昌学院学报（自然科学版）》2021年第1期58-61,99,共5页Journal of Xichang University(Natural Science Edition)

基　　金：安徽省高校自然科学研究项目(KJ2017A704);亳州学院自然科学研究项目(BYZ2019B03);亳州学院精品课程《线性代数》(2017jpkc04);亳州学院教研项目(2017ybjy22);亳州学院科研项目(bsky201430)。

摘　　要：以四元数的实表示为基础,结合爪形矩阵的结构特点,利用矩阵的拉直与Kronecker积,将爪形矩阵约束四元数矩阵方程AXB=C转换成无约束的实矩阵方程,得出其有自共轭解的充要条件及通解表达式。最后,在给定的解集中,求得已知四元数爪形矩阵有极小Frobenius范数的最佳逼近解。Based on the real representation of quaternion,combined with the structural characteristics of the claw matrix,and through the Kronecker product of matrices,the constrained quaternion matrix equation AXB=C of the claw matrix is transformed into the unconstrained real matrix equation.Then the necessary and sufficient conditions for the existence of a paw form matrix solution and a self-conjugate paw form matrix solution of the equation are obtained.Finally,the optimal approximation of the minimum Frobenius norm for the given quaternion claw matrix in the given solution set is obtained.

关 键 词：四元数体 实表示 KRONECKER积 自共轭解 最佳逼近 

分 类 号：O241.6[理学—计算数学]