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
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,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.