广义对称、反对称矩阵反问题

时间:2017-08-11 数学毕业论文 我要投稿

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

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