关于线性子空间与仿射子空间的注记  

Notes on Linear and Affine Subspaces

作　　者：徐运阁 曾祥勇 XU Yun-ge;ZENG Xiang yong(Faculty of Mathematics and Statistics,Hubei University,Hubei Key Laboratory of Applied Mathematics Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院应用数学湖北省重点实验室,武汉430062

出　　处：《大学数学》2018年第4期68-72,共5页College Mathematics

基　　金：湖北大学教学研究项目(201749);湖北省教育厅教改项目(2017)

摘　　要：作为线性方程组的逆问题,本文刻划了线性子空间与仿射子空间分别是某一齐次与非齐次线性方程组的解集,并给出了利用矩阵初等行变换求解相应线性方程组的简便方法;进一步通过仿射子空间引入商空间的概念,建立线性空间的同态基本定理,从而得到维数公式的一个新的证明.Considered as an inverse problem to system of linear equations, linear and affine subspaces are characterized to be the solution sets of homogeneous and non homogeneous systems of linear equations respectively, and a very convenient way to solve the inverse problem is given based on row elementary transformations of matrices. Furthermore, quotient spaces are introduced via affine subspaces, the homomorphism fundamental theorem is established and thus a new proof for the dimension formula is obtained.

关 键 词：线性子空间 仿射子空间 商空间 维数公式 

分 类 号：O151.2[理学—数学]