四元数矩阵的实表示与四元数矩阵方程

Real Representiations of Quaternion Matrices and Quaternion Matrix Equations

四元数矩阵与四元数矩阵方程在力学和工程问题的理论研究和实际数值计算中都起到重要的作用．该文借助四元数矩阵的实表示方法,研究了一般四元数矩阵方程AXB-CYD=E的解的问题,给出了一种求解四元数矩阵方程的算法技巧．该文还得到了四元数矩阵的Roth's定理．

Quaternion matrices and quaternion matrix equations play important roles in quantum mechanics. By introducing real representations of quaternion matrices, this paper studies the solution of the general quaternion matrix equation AXB - CYD = E, and gives a prectical technique of finding the solution of the quaternion matrix equation. This paper also obtains a Roth＇s theorem over the quaternion field.