矩阵方程A^TXA=C的对称斜反对称最小二乘解  

Symmetric and skew-antisymmetric least square solutions of matrix equation A^TXA=C

作　　者：吴文静[1] 康素玲[1] 

机构地区：[1]合肥学院数理系,安徽合肥230022

出　　处：《合肥工业大学学报（自然科学版）》2010年第4期629-631,640,共4页Journal of Hefei University of Technology：Natural Science

基　　金：合肥学院自然科学基金资助项目(10KY01ZR;09KY03ZR)

摘　　要：文章利用矩阵对的广义奇异值分解和对称斜反对称矩阵的性质,研究了矩阵方程ATXA=C的对称斜反对称最小二乘解,并给出其通解的表达式;由正交矩阵的性质进一步给出了在相应的对称斜反对称最小二乘解解集中该矩阵方程的极小范数解。By applying the generalized singular value decomposition（GSVD） of matrix pairs and the properties of symmetric and skew-antisymmetric matrix, the expression of the symmetric and skew- antisymmetric least square solutions of the matrix equation A^TXA=C is given in this paper. In addition, according to the property of orthogonal matrix, the explicit expression of minimum norm solution is also derived in the corresponding symmetric and skew-antisymmetric solution set of the matrix equation.

关 键 词：矩阵方程 对称斜反对称矩阵 最小二乘解 极小范数解 

分 类 号：O175.13[理学—数学]