【摘要】 <正> 1 引言 令R^n×m表示所有n×m实矩阵集合,R_n^n×n表示所有n阶可逆方阵集合,OR^n×n表示所有n阶正交矩阵的集合,SR^n×n表示所有n阶实对称矩阵集合,I_n表示n阶单位矩阵,rank（A）表示矩阵A的秩,||·||表示矩阵的Frobenius范数,A*B表示矩阵A与B的Hadamard乘积,其定义为A*B=(a_ijb_ij),其中A=(a_ij),B=(b_ij)∈R^n×n。更多还原

【Abstract】 By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric ortho-symmetric solutions of the linear matrix equation ATXA=B. In addition, the expression of the optimal approximation solution to the given matrix is derived.更多还原