矩阵方程AX=B的自反最小秩解及其最佳逼近  

The reflexive minimal rank solution of the matrix equation AX = B and the optimal approximation

作　　者：肖庆丰[1] 胡锡炎[2] 张磊[2] 

机构地区：[1]东莞职业技术学院公共教学部,广东东莞523808 [2]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《纯粹数学与应用数学》2012年第6期719-727,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(10571047);高校博士学科点专项科研基金(20060532014)

摘　　要：利用矩阵对的广义奇异值分解,得到了矩阵方程AX=B有自反解的充分必要件,以及有解时,定秩解、最小秩解的一般表达式.另外,给出了自反最小秩解集合中与给定矩阵的最佳逼近解.By applying the generalized singular value decomposition of matrix pairs, the necessary and sufficient conditions are obtained for the existence of the reflexive solutions of the matrix equation AX = B, and the expression of the fixed and minimal rank solutions is also shown. In addition, for the minimal rank solution set, the expression of the optimal approximation solution to a given matrix is derived.

关 键 词：矩阵方程 自反矩阵 广义奇异值分解 最小秩解 最佳逼近 

分 类 号：O241.6[理学—计算数学]