弱双四元数广义Sylvester方程的混合解

The Mixed Solution of Reduced Biquaternion Generalized Sylvester Equation

利用矩阵半张量积、弱双四元数矩阵的复矩阵表示以及特殊矩阵的H-表示方法对弱双四元数广义Sylvester方程的混合解进行研究。利用H-表示方法提取特殊矩阵的独立元素,从而去除冗余。结合矩阵半张量积、弱双四元数矩阵的复矩阵表示将弱双四元数Sylvester方程转化为具有独立变量的复矩阵方程。由经典矩阵理论给出广义Sylvester方程存在混合解的充要条件及通解表达式。通过数值算例验证该方法的有效性。

The mixed solution of reduced biquaternion generalized Sylvester equation is studied by using semi-tensor product of matrices,complex matrix representation of reduced biquaternion matrix and H-representation of special matrix.The independent elements of special matrix are extracted by H-representation method to remove the redundancy.Combined with the semi-tensor product of matrices and complex representation of reduced biquaternion matrix,the reduced biquaternion Sylvester equation is transformed into a complex matrix equation with independent variables.The necessary and sufficient conditions for the existence of the mixed solution and the expression of general solution of generalized Sylvester equation are given by classical matrix theory.A numerical example is given to verify the effectiveness of the method.