| 线性子空间的并集完全不覆盖的基 |
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| 引用本文： | 汪杏枝.线性子空间的并集完全不覆盖的基[J].湖北师范学院学报(自然科学版),2006,26(1):22-25. |
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| 作者姓名： | 汪杏枝 |
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| 作者单位： | 湖北师范学院,数学系,湖北,黄石,435002 |
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| 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。
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| 关 键 词： | 线性空间 欧氏空间 真子空间 标准正交基 可数 |
| 文章编号： | 1009-2714(2006)01-0022-04 |
| 收稿时间： | 07 5 2005 12:00AM |
| 修稿时间： | 2005年7月5日 |
Completely uncovered basis in linear subspace set |
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| WANG Xing-zhi.Completely uncovered basis in linear subspace set[J].Journal of Hubei Normal University(Natural Science),2006,26(1):22-25. |
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| Authors: | WANG Xing-zhi |
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| Institution: | Department of Mathematics, Hubei Normal University, Huangshi 435002, China |
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| Abstract: | 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 -dimensional 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 m orthonormal basis completely uncovered by M. |
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| Keywords: | linear space Euclidean space subspace orthonormal basis denumerable |
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