线性无关

When learning completed, the outputs of different units in the same hidden layer are irrelative.

这种学习算法是基于下面基本事实：同一隐层神经单元对不同输入的响应所构成的向量组应线性无关。

Having a texture composed of lath - shaped plagioclase crystals in a matrix of pyroxene crystals.

我们把这个矩阵的秩定义为它所包含的线性无关行的数目。

This paper shows that the Lebesgue measure of the singular matrices in R\+\{n×n\} is zero.

证明了 n阶实矩阵集合中奇异矩阵集合的勒贝格测度等于零，n维实空间中 m个随机向量线性无关的概率为

Taking into account the orthogonality and linear independence of trigonometric functions, closed-form expressions for scattering coefficients are developed by imposing continuity conditions of pile-soil interfaces and equilibrium conditions of piles.

通过施加问题的连续条件和平衡条件，利用三角函数的正交性以及不同阶三角函数线性无关的性质，得到问题的解。

Another reason is that the degree of linear independence of the variable basis functions composed by sigmoid functions decreases as the hidden nodes increasing, and this lead up to the inferior matrix condition number during learning, which forces the learning step length to decrease and the convergence speed to slow down.

一是因为未知系统复杂时需要较多的隐节点，从而学习的参数过多减慢了学习速度；另一个原因是随着隐节点数增加，由Sigmoid函数构造的可变基函数线性无关程度减弱，从而导致学习过程中矩阵条件数变差，迫使学习步长减小，收敛速度不得不减慢。

In theory we require linear independence among variables used as inputting or outputting of BP net when we model the mineral processing plant with BP net. However it is always definite relativity in inputting variables or outputting variables in modeling of the mineral processing plant, which sets definite obstacle in high quality modeling.

在应用BP网络建立选矿厂数学模型时，理论上要求作为BP网络的输入变量之间或输出变量之间应是线性无关的，而选矿厂数学建模中，输入变量之间或输出变量之间往往存在着一定的相关关系，这对建立高质量的模型设置了一定的障碍。

First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a low dimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space.

首先分析主成分分析法产生非光谱数据的原因，据此对经典主成分分析模型增加非负约束；然后求出一组线性无关的非负主成分权向量，用该组向量构造低维空间；最后用非线性优化技术确定高维数据在该低维空间中的投影值，实现了高维空间与低维空间的相互转换。

Chapter2, mainly summarizing the optimality conditions for the nonconvex semidefinite programming, first recalls the concept of transversality condition, proves that transversality condition and linear independence condition are equivalent, and shows that under strict complementarity condition, the transversality condition is a sufficient condition for uniqueness of the Lagrange multipliers.

第2章，主要综述非凸半定规划的最优性条件，首先回顾了横截性条件的概念，证明了横截性条件与线性无关条件是等价的。并且说明了在严格互补松弛条件下，横截性条件是Lagrange乘子矩阵唯一的充要条件。

A system that can uniquely represent any unit which can be composed from a linearly independent set of base units.

对於可以分解为一组线性无关的基础单位的单位可以惟一表示的系统。

The first n searches are along each of a set of linearly independent directions.

第一批n个搜索是沿线性无关方向集中的每一个方向的。

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。