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矩陣的廣義逆及其應(yīng)用
矩陣的廣義逆及其應(yīng)用
摘要
本文首先對(duì)矩陣的廣義逆進(jìn)行定義及其分類，然后詳細(xì)討論每1類廣義逆矩陣的性質(zhì)及其求解方法，其中包括減號(hào)逆 的性質(zhì)與求解，自反減號(hào)逆 （左逆 與右逆 的性質(zhì)與求解）以及加號(hào)逆 的唯1性證明與求解。通過對(duì)每1類廣義逆矩陣的求解方法的研究，最后探討矩陣的廣義逆在解線形方程組中的應(yīng)用。
關(guān)鍵字：廣義逆矩陣；滿秩長(zhǎng)矩陣；初等變換；線形方程組。
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.
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