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