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........................................................................................................32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OnthecomparisonoflinearspaceandEuclideanspaceAbstractLinearspaceandEuclideanspaceis"HigherAlgebra"isthetwoimportantparts,theyaredifferentandcontact,abriefdescriptionofthedefinition,conceptandcharacteristicsofthem,andfromtheirbasicdomains,operation,matrix,vectorcoordinate,lineartransformationofseveralaspectsofthediscussionthan.【Keywords】Euclideanspacelinearspacecontrast1绪论1.1研究目的与研究意义线性空间与欧式空间是《高等代数》中两部分重要内容,两者既有区别又有联系。本论文旨在从不同的方面对其进行比较与讨论。在线性空间中,向量之间的基本运算只有加法与数量...