求生成子空间的交的一种方法  

A Way to Seek the Intersection Set of Two Generated Subspaces

作　　者：陈之辉 CHEN Zhi-hui(School of Mathematics and Statistics,Cangzhou Normal University,Cangzhou,Hebei 061001,China)

机构地区：[1]沧州师范学院数学与统计学院,河北沧州061001

出　　处：《沧州师范学院学报》2018年第1期1-4,共4页Journal of Cangzhou Normal University

摘　　要：线性空间中两组向量各自生成一个子空间,这两组向量分别由另外同一组向量线性表示,分别求出相应的表示矩阵.由这两个表示矩阵构造一个齐次线性方程组并求出其基础解系.最初的两组向量中的任意一组与该齐次线性方程组中相应的未知量在基础解系中每个解向量里的取值作线性组合得出若干个向量,这若干个向量生成的子空间即为最初两个生成子空间的交.Each of two groups of vectors in linear space generates a subspace.Each of the two is represented linearly by another same group of vectors and two representing matrixes are worked out correspondingly.On the basis of the two representing matrixes,a system of homogeneous linear equations are established and the system of fundamental solutions of the system of homogeneous linear equations are calculated out.Any of the two groups of vector given initially combine with the value taken by corresponding unknown quantities of the system of homogeneous linear equations in every solution vector of the system of fundamental solutions,then several vectors are produced.The subspace generated by these vectors is the intersection set of the two generated subspaces given initially.

关 键 词：子空间 交 齐次线性方程组 基础解系 

分 类 号：O177.3[理学—数学]