矩阵的广义逆及其应用

矩阵的广义逆及其应用

摘要

本文首先对矩阵的广义逆进行定义及其分类，然后详细讨论每1类广义逆矩阵的性质及其求解方法，其中包括减号逆 的性质与求解，自反减号逆 （左逆 与右逆 的性质与求解）以及加号逆 的唯1性证明与求解。通过对每1类广义逆矩阵的求解方法的研究，最后探讨矩阵的广义逆在解线形方程组中的应用。

关键字：广义逆矩阵；满秩长矩阵；初等变换；线形方程组。

Ｇeneralized Inverse Matrices and Its Application

ABSTRACT

Firstly,this paper deals with the definition and classification of generalized inverses; then, the characteristics and solutions of all kinds of generalized inverses , including A-,Ar-,A+, have been discussed;lastly, the application of generalized inverse in solving linear equations has been narrated.

Key word: generalized inverse matrices ,full ring matrix, elementary grade transformation, the line form square distance set.