论线性空间与欧氏空间的对比

Discussion on the Contrast between Linear Space and Euclid Space

线性空间与欧氏空间是《高等代数》的两部分重要内容,两者之间既有区别又有联系,从它们的基础域、运算、基、向量的坐标、过渡矩阵、线性变换、子空间和同构8个方面进行对比讨论。

Vector space and Euclid space are two important parts in the study of advanced algebra . They are different but also closely connected with each other, We discuss them from the following eight aspects： base area, operation, radix, coordinates of vectors, Transational matrix, linear counter chanange subspace and isomorphism