由给定的子空间构造新的子空间

On Constructing New Vector Subspaces by Given Subspaces

本文给出并证明了若干个子空间的并以及两个子空间的差构成子空间的充要条件 ,从而本质地揭示了除子空间的交与和是构造新的子空间的方法外 ,集合的其它运算不能构造新的子空间 ,最后分析了子空间直和的两种不同定义的优缺点 ,指出了张禾瑞教材中子空间直和定义推广时应注意的一个问题 .

n this paper,we present and prove sufficient and necessary conditions of consisting of new subspaces from the union and difference of subspaces.Thereby it is revealed essentially that except for the intersection and sum of subspaces,the other operations of subspaces are not mthods of constructing new subspaces.Finally,we analyze the advantage and disadvantage of two definitions ofthe direct sum of subspaces,and piont out that one should note a problem on generalizing the definition of direct sum from the case of two subspaces to that of multi-subspaces in the texbook of Zhang et al.