目录1绪论.............................................................................................................................31.1研究目的与研究意义.......................................................................................31.2研究现状...........................................................................................................31.3研究内容...........................................................................................................32欧式空间简介.............................................................................................................42.1提出背景...........................................................................................................42.2定义与基本性质...............................................................................................52.3度量矩阵...........................................................................................................82.4标准正交基.......................................................................................................92.5同构.................................................................................................................122.6正交变换.........................................................................................................162.7对称变换.........................................................................................................193线性空间简介...........................................................................................................213.1线性空间的概念.............................................................................................223.2线性变换的定义.............................................................................................223.3线性变换的性质和运算.................................................................................233.4线性变换的矩阵.............................................................................................244线性空间与欧式空间的对比...................................................................................284.1基础域的对比讨论.........................................................................................284.2运算的对比讨论.............................................................................................294.3基的对比讨论.................................................................................................294.4向量坐标的对比讨论.....................................................................................294.5线性变换的对比讨论.....................................................................................294.6同构的对比讨论.............................................................................................30参考文献......................................................................................................................31致谢............................................................................................................................32I论线性空间与欧式空间的对比摘要线性空间与欧式空间是《高等代数》的两部分重要内容，两者之间既有区别又有联系，简要描述他们的定义、概念、特征，并从它们的基础域、运算、基、向量的坐标、线性变换、同构几个方面进行对比讨论。【关键词】欧式空间线性空间对比1OnthecomparisonoflinearspaceandEuclideanspaceAbstractLine...
