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

作　　者：张琴[1] 王卿文[1] 常海霞[2] 

机构地区：[1]上海大学数学系,上海200444 [2]上海金融学院,上海201209

出　　处：《数学物理学报（A辑）》2010年第3期743-752,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(60672160);上海市教委创新基金(09YZ13)和上海市教委重点学科建设项目(J50101)资助

摘　　要：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.

关 键 词：四元数 四元数矩阵 MOORE-PENROSE逆 矩阵方程组 广义反射矩阵 

分 类 号：O151.21[理学—数学]