有限维向量空间

当V是实数域上的有限维向量空间，g（x，y）是正定对称纯量积时，本文给出了用矩阵的初等变换得到笛卡尔基的方法。

When Visa finite dimensional vector space over the field of real numbers , g ( x , y ) is a positive definite symmetric scalar product , This article gives a method to get a Cartesian basis by the elementary transformations of matrices .

进一步，为了推导新的恒等式，我们引入了theta分解的概念，说明了给定邻接关系的theta函数解空间可以转化为域K（q）上的有限维向量空间。

Furthermore , we introduce the notion of theta decompositions to derive new theta function identities . We explain how to transform the set of the theta function solutions of a given contiguous relation into a finite dimensional vector space over the field K ( q ) .

引进有限维向量空间的（s，k）-较多序类概念，并给出它们的基本性质。

In this paper the authors have introduced the ( s , k ) - major order class concept in the finite-dimension vector space and given their basic properties .

有限维向量空间中基的选取

Basis Selection in Limited Dimension Vector Space

最后，我们给出有限维向量空间中对称双线性型非退化的简单条件。

Finally , we give a simple condition for nondegeneracy of symmetric bilinear forms on infinite dimensional vector spaces .

有限维向量空间中选取基时需注意三个因素：1.用基体现子空间之间的关系；

There are three factors need to be noticed when the basis is selected in limited dimension vector space : 1.reflecting the relationships among subspaces by basis ;

该文利用矩阵的初等变换解决有限维向量空间中向量组的线性性质的有关问题，并给出了这种方法的理论依据。

This paper with elementary transformation of matrix discusses some properties of a set of vectors in finite dimensional vector space and the theory basis of this method is given .

应用矩阵初等变换的一些性质解决有限维向量空间中若干问题和求两个多项式的最大公因式。

The purpose of this paper is to use properties of elementary transformation of matrix to solve some problems of finite dimensional vector space and to get the greatest common factor of two polynomials .