| 弱正交补的唯一性及其应用 |
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| 引用本文： | 徐德余. 弱正交补的唯一性及其应用[J]. 绵阳师范学院学报, 2006, 25(5): 3-4,45 |
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| 作者姓名： | 徐德余 |
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| 作者单位： | 绵阳师范学院数学与信息科学系,四川,绵阳,621000 |
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| 摘 要： | 在一般的线性空间中引入弱内积,使之成为弱内积空间,再引入弱正交、弱正交补概念,证明了任何数域上的线性空间都是弱内积空间、任何弱内积空间的子空间都有唯一的弱正交补,并给出了齐次线性方程组同解的一个充分必要条件。
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| 关 键 词： | 弱内积 弱内积空间 弱正交 弱正交补 唯一性 |
| 文章编号： | 1672-612x（2006）05-0003-02 |
| 收稿时间： | 2006-09-03 |
| 修稿时间： | 2006-09-03 |
The Uniqueness of Weak Orthogonal Complement and Its Applications |
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| XU De-yu. The Uniqueness of Weak Orthogonal Complement and Its Applications[J]. Journal of Mianyang Normal University, 2006, 25(5): 3-4,45 |
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| Authors: | XU De-yu |
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| Affiliation: | Department of Mathematics and Information Science, Mianyang Normal University, Mianyang,Sichuan 621000 |
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| Abstract: | By introducing first the concept of weak inner and weak orthogonal complement,we have testified the uniqueness of weak orthogonal complement and finally give the necessary and sufficient condition for the same solution of the homogeneous linear equations. |
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| Keywords: | weak inner product weak inner product space weak orthogonal weak orthogonal complement uniqueness |
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