广义对称、反对称矩阵反问题

广义对称、反对称矩阵反问题

广义对称、反对称矩阵反问题

摘要

本文定义了实数域R上的两类广义对称和反对称矩阵集合．利用矩阵的Moore-Penrose广义逆和广义奇异值分解，给出了在所定义的两类广义对称和反对称矩阵集合中矩阵反问题AX=B有解的充分必要条件及有解时解的1般表达式．
关键词：广义对称矩阵；广义反对称矩阵；广义奇异值分解；最佳逼近；反问题

The Inverse Problem of Generalized Symmetric and Anti-symmetric Matrix

ABSTRACT

This paper two kinds of generalized symmetric and anti-symmetric matrix sets are defined. By applying the Moore-Penrose generalized inverse and the decomposition of generalized singular value of matrices, the necessary and sufficient condition for the inverse problem AX=B have a solution in given matrix sets are derived. And the general expression for the solution of the problem are also given.
Keywords: generalized symmetric matrix; generalized anti-symmetric matrix; the decomposition of generalized singular value; optimal approximation; inverse problem

【广义对称、反对称矩阵反问题】相关文章：

求实对称矩阵特征值问题的分治算法03-07

矩阵方程的自反和反自反矩阵解03-07

数学毕业论文-求实对称矩阵特征值问题的分治算法11-19

浅谈广义次正定矩阵03-07

矩阵的广义逆及其应用03-07

关于保险信息不对称问题的探讨03-21

市场与反市场的两类不同问题03-11

电子商务中信息不对称问题研究03-18

浅析当前电子商务中信息不对称问题03-18