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楚雄师范学院本科论文（设计）

目录

摘 要： .......................................................................................................................................................... I 关键词： .......................................................................................................................................................... I Abstract ......................................................................................................................................................... II Keywords： .................................................................................................................................................. II 1．前言 ........................................................................................................................................................... 1 2．预备知识 ................................................................................................................................................... 1 2.1线性相关性的概念及性质 .................................................................................................................. 1

2.1.1线性相关的概念 ............................................................................................................................ 1 2.1.2线性相关的性质 ............................................................................................................................ 2 3.向量组线性相关的判定方法 ..................................................................................................................... 3 3.1定义法 .................................................................................................................................................. 3 3.2根据齐次线性方程组的解进行判定 .................................................................................................. 4 3.3利用矩阵的秩进行判定 ...................................................................................................................... 5 3.4利用行列式值进行判定 ...................................................................................................................... 6 3.5反证法 .................................................................................................................................................. 7 3.6 数学归纳法 ......................................................................................................................................... 7 3.7用线性变换的性质进行判定 .............................................................................................................. 8 3.8利用朗斯基行列式来判定 ................................................................................................................ 10 4.结束语 ........................................................................................................................................................ 11 参考文献 ....................................................................................................................................................... 12 致谢 ............................................................................................................................................................... 13

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楚雄师范学院本科论文（设计）

向量组的线性相关性的判定方法浅析

摘 要：本文总结综述了向量组线性相关性的判定方法，并阐述了不同判定方法适用的条件.

关键词：线性相关；线性无关；判定方法.

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楚雄师范学院本科论文（设计）

Several Methods of Judging the Linear Dependence of A Vector

Group is analysed

Abstract：This article summarizes the judging methods of vector linear correlation, and expounds the different methods applicable conditions.

Keywords：linear correlation; linear independence; judging methods .

II