一四元数矩阵方程组的广义(反)反射解

The Generalized(Anti) reflexive Solutions to a System of Quaternion Matrix Equations

该文给出了四元数矩阵方程组X_1B_1=C_1,X_2B_2=C2,A_1X_1B_3+A_2X_2B_4=C_b可解的充要条件及其通解的表达式,利用此结果建立了四元数矩阵方程组XB_a=C_a,A_bXB_b=C_b有广义(反)反射解的充要条件及其有此种解时通解的表达式.

We give necessary and sufficient conditions for the existence of the general solution to the system of quaternion matrix equations X1B1=C1,X2B_2=C2,A1X1B3＋A2X2B_4=Cb. When the solvability conditions are met,we present an expression of the general solution to this system.Using the results on this system,we investigate necessary and sufficient conditions for the existence of generalized reflexive and generalized antireflexive solutions to the system of quaternion matrix equations XBa=Ca and AbXBb=Cb.We present expressions of the generalized reflexive and generalized antireflexive solutions to the system mentioned above when the solvability condtions are satisfied.