摘要
在n维线性空间V中,对于有限个真子空间的并集M,都存在V的一个无穷子集U使得M完全不能覆盖U,并且U中的任何的n个元都是V的基。在不可数数域上的n维线性空间V中,对于可数个真子空间的并集M,都存在V的一个无穷子集U使得M完全不覆盖U,并且U中的任何的n个元都是V的基。在n维欧氏空间V中,对于可数个真子空间的并集M,都存在V的一个可数的无穷子集所作成的序列U,使得M完全不覆盖U,并且U中含有V的标准正交基,U中任何的,n个相连的元都是V的基；对于任何的正整数m,V有m个标准正交基完全不被M覆盖。
In n -dimensional linear space V,limited subspace join M has a infinite subset U of V, which makes M completely not cover U, and any n element in U is the base of V. In non - denumerable number field, the denumerable subspace join M has a infinite subset U of V, which makes M completely not cover U, and any n elements in U is the base of V. In n - dimensiomd Euclidean space V, denumerable subspace join M has a denumerable infinite subset U, which makes M completely not cover U, and U contains orthonormal basis of V, any n elements of connected in U is the base of V,any postive integer m, V has ,n orthonormal basis completely uncovered by M.
出处
《湖北师范学院学报（自然科学版）》
2006年第1期22-25,共4页
Journal of Hubei Normal University(Natural Science)
关键词
线性空间
欧氏空间
真子空间
标准正交基
可数
linear space
Euclidean space
subspace
orthonormal basis
denumerable
