基于矩阵半张量积求解弱双四元数矩阵方程AX=B

Solve the Reduced Biquaternion Matrix Equation AX=B Based on Semi-tensor Product of Matrices

利用矩阵半张量积方法研究弱双四元数矩阵方程AX=B的解,通过提出一种新的实向量表示,将弱双四元数矩阵方程问题转化为相应实矩阵方程问题.由此得到弱双四元数方程AX=B的最小二乘解、相容条件及通解表达式,并给出相应的算法,通过数值实验检验了算法的有效性.

In this paper,the solution of reduced biquaternion matrix equation AX=Bis studied by using the method of semi tensor product of matrices.By proposing a new real vector representation of reduced biquaternion matrix,the problem of reduced biquaternion matrix equation is transformed into the corresponding real matrix equation.The least square solution,compatibility condition and general solution expression of reduced biquaternion matrix equation AX=B are obtained,and the corresponding algorithm is given.The effectiveness of the algorithm is verified by numerical experiments.