线性无关

From Poisson matrix, we can observe volume-preserving vector fields. By using Geiges-Gonzalo's existence of contact circle Theorem [3] , we show the existence of volume-preserving circle on3-manifolds which says that every3-manifold admits two linear independent vector fields preserving a same volume form.

通过Poisson矩阵可以观察出保积向量场，再利用Geiges-Gonzalo的接触圆存在性定理[3]，我们证明了保积圆的存在性：每个闭的3-流形上都存在两个处处线性无关的保积向量场并且它们的常系数线性组合仍是保积向量场。

We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between F_q and F_ denoted by F_ where s divides t. The polynomials we constructed are F_q-linearly independent and return elements in F_q when they are evaluated at elements of the extension fields.

结合Reed-Solomon码的构造特点，我们将Chaoping Xing与San Ling所构造的线性码的方法推广到有限域的任意次扩张上，首先利用正规元和循环排列来构造系数属于F_q和F_q的任意次扩域F_之间的中间域的具有特殊性质的多项式，中间域记为F_，其中s为t的真因子，由正规元的选择可以保证所构造多项式的F_q-线性无关性，并且这些多项式在扩域F_中取值都属于F_q，从而构造出一类q元线性码。

Aim To generate the concepts and properties of linear dependence and linear independence.

目的 推广线性相关与线性无关的定义与性质。

Results and Conclusion The concepts of strong linear dependence and weak linear independence are introduced, their some properties and distinguishing method are given, and some results of linear space are obtained.

结果／结论引入了强线性相关与弱线性无关的定义，给出了它们的性质和判别方法，并得到线性空间的一些结论。

This thesis is devoted to study the properties of the solutions of some specialrefinable equations,such as properties of multi-refinable,global linear independence,local linear independence and local polynomial property,etc,by using fractal theory,measure theory and theory of generalized functions.

本文的主要目的是通过用分形几何中的一些想法以及测度论和广义函数中的一些知识来研究一些特殊的细分方程的解的一些性质，如多重可细分性、整体线性无关性、局部线性无关性和局部多项式性质等。

If deg f = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in ?

证明了，若degf=n，则R_f~c为空集，对于所有的二次布尔函数而言，均有R_f~c中的元素个数大于等于2~(n-1)，给出了R_f构成线性子空间时，R_f和L_f之间的关系，还给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素。

We apply this general result to Vamos matroid and obtain a family of non-representable multipartite matroids.

我们将这一结论应用于Vamos拟阵，于是得到了一族不可表示的多部拟阵，同时我们利用向量的线性相关和线性无关性对Vamos拟阵的不可表示性给出了新的证明。

Deduce that the columns of a square matrix are linearly independent if and only if the rows are.

推导若且唯若一方阵的列向量为线性无关，则其行向量为线性无关。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

We get a class of refinable distributions which have localpolynomial property and are globally linear independent but are locally lineardependent,So that when M＞N,the Daubechies type scaling functions〓have localpolynomial properties and are globally linear independent but locally lineardependent.

给出了一类细分方程，它们的解具有局部多项式性质并且它们是整体线性无关的但是它们是局部线性相关的。从而得到了当〓时，Daubechies型尺度函数〓具有局部多项式性质并且它们是整体线性无关的但是它们是局部线性相关的。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。