基于矩阵半张量积解特殊结构的四元数线性系统

Solution of Quaternion Linear System with Special Structure Based on Semi-tensor Product of Matrices

提出一种四元数的实向量表示,借助矩阵半张量积研究具有特殊结构的四元数Toeplitz线性系统Ax=b,得到了有解的充要条件及四元数线性系统相容时的通解表达式,并给出了数值例子来检验方法的有效性.

In this paper, a real vector representation of quaternion was proposed. A Toeplitz linear system of quaternion Ax=b with special structure was studied by means of semi-tensor product of matrices. The necessary and sufficient conditions for the existence of solutions and the expression of general solution of quaternion linear system were obtained. Furthermore, numerical example was given to verify the effectiveness of the method.