有限维线性空间上子空间并的性质的一个注记  

One Notes Upon the Property of the Union of Subspaces of the Finite Dimensional Linear Space

作　　者：孙丽雪[1] 李永彬[1] 林晨[1] 

机构地区：[1]电子科技大学数学科学学院,四川成都611731

出　　处：《大学数学》2014年第4期29-32,共4页College Mathematics

摘　　要：对于特征为零的域上的有限维线性空间的子空间的并,我们知道下述性质:有限个互不包含的非平凡子空间的并不是原来的线性空间.一方面,本文通过介绍有限维线性空间中任一子空间与齐次线性方程组解子空间的关系,及商空间的维数公式,给出了上述性质的一个改进证明.另一方面,本文把仿射簇的概念和子空间联系起来,并根据仿射簇的一个简单性质,给出了上述性质的另一个更为简洁的证法.For the union of subspaees of the finite dimensional linear space over the field whose characteristic is zero, we know the following property： the union of finite non--trivial subspaces which do not include each other is not the original linear space. On one hand, this paper through presenting the relation between any suhspace of the finite dimensional linear space and the subspace of solutions of homogeneous linear equations, and the dimension formula of quotient space,gives an improving proof of the property. On the other hand, hy eomhining the definition of the affine variety with the subspace,and according to a simple property of the affine variety,this paper presents a simpler proof of the property.

关 键 词：子空间 商空间 维数公式 子空间的并 特征 仿射簇 

分 类 号：O143[理学—数学]