基于矩阵半张量积求解四元数Toeplitz线性系统  

Solving quaternion Toeplitz linear system based on semi-tensor product of matrices

作　　者：李莹[1] 王玉珊 丁文旭 韦安丽 LI Ying;WANG Yushan;DING Wenxu;WEI Anli(College of Mathematics Science,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《安徽大学学报（自然科学版）》2022年第3期47-52,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(62176112);山东省科技厅自然科学基金资助项目(ZR2020MA053);聊城大学科研基金资助项目(318011921)。

摘　　要：针对四元数上三角Toeplitz线性系统的求解问题,提出了一种利用四元数矩阵的实向量表示与矩阵半张量积的新方法,给出四元数上三角Toeplitz线性系统相容的充要条件及通解表达式,通过数值算例检验了该方法的有效性.In this paper,for solving quaternion upper triangular Toeplitz linear system,a new method was proposed by using the real vector representation of quaternion matrix and the semi-tensor product of matrices.The necessary and sufficient conditions and the general solution expression of the quaternion upper triangular Toeplitz linear system were given.The effectiveness of the method was verified by numerical examples.

关 键 词：四元数线性系统 MOORE-PENROSE逆 实向量表示 矩阵半张量积 TOEPLITZ矩阵 

分 类 号：O151.21[理学—数学]