【摘要】 <正>1引言首先引入一些记号.记C^n×m为n×m复矩阵的集合.UC^n×n表示所有n阶酉矩阵的集合.I_n表示n阶单位矩阵.A^H和A⁺分别表示矩阵A的共轭转置及Moore-Penrose广义逆.对A=(a_ij)_s×t,B=(b_ij)_s×t,用A*B=(a_ijb_ij)_s×t表示A与B的Hadamard积.矩阵A,B的内积定义为（A,B）=tr（B^HA）,由此内积诱导的范数为‖A‖=（A,A）^1/2=（tr（A^HA））^1/2,则此范数为Frobenius范数,并且C^n×m构成一个完备的内积空间.更多还原

【Abstract】 Let R∈C^n×n be a nontrivial generalized reflection matrix satisfying R=R^-1≠±I_n.G∈C^n×n is said to be generalized centrosymmetric if RGR=G. The set of all n×n generalized centrosymmetric matrices is denoted by GCSC^n×n. In this paper,a sufficient and necessary condition for the matrix equation XA-YB=D having a solution X,Y∈GCSC^n×n is derived,and the general solutions are given.The optimal approximation between given matrix■ and the offine subspace of solutions to the matrix equation is discussed,an explicit representation of the unique optimal approximation solution is presented,and a numerical example is provided.更多还原