秩约束下矩阵方程AX=B的反对称解及其最佳逼近(英文)  

THE RANK-CONSTRAINED ANTI-SYMMETRIC 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：《数学杂志》2013年第5期803-810,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10571047);the Doctorate Foundation of the Ministry of Education of China(20060532014)

摘　　要：本文研究了秩约束下矩阵方程AX=B的反对称解问题.利用矩阵秩的方法,获得了矩阵方程AX=B有最大秩和最小秩解的充分必要条件以及定秩解的表达式,同时对于最小秩解的解集合,得到了最佳逼近解.In this article, we study the anti-symmetric solutions with prescribed ranks to the matrix equation AX = B. By applying the matrix rank method, we present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions which is anti- symmetric to the equation. The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, corresponding to the minimal rank solution set to the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is provided.

关 键 词：反对称矩阵 矩阵方程 最大秩 最小秩 定秩解 最佳逼近解 

分 类 号：O241.6[理学—计算数学]