矩阵方程AX=B的中心对称定秩解及其最佳逼近（英文）  

CENTRO-SYMMETRIC MINIMAL RANK SOLUTIONS AND ITS OPTIMAL APPROXIMATION OF THE MATRIX EQUATION AX=B

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：《数学杂志》2015年第3期505-512,共8页Journal of Mathematics

摘　　要：本文研究了矩阵方程AX=B的中心对称解.利用矩阵对的广义奇异值分解和广义逆矩阵,获得了该方程有中心对称解的充要条件以及有解时,最大秩解、最小秩解的一般表达式,并讨论了中心对称最小秩解集合中与给定矩阵的最佳逼近解.The centro-symmetric solutions of the matrix equation AX = B are considered. By using the generalized singular value decompositions of matrix pairs and generalized inverses of matrices, necessary and sufficient conditions for the existence of such solution and the expression of the maximal and minimal rank solutions are derived. Also, the optimal approximation for the minimal rand solution set to a given matrix is also discussed and the expression of the solution is presented.

关 键 词：矩阵方程 中心对称矩阵 最大秩解 最小秩解 最佳逼近解 

分 类 号：O241.6[理学—计算数学]