向量的模

构造了C1插值的平面三次PH样条曲线，使得平面三次PH曲线能够对切向量的模长插值，拓宽了其在机器人路径的设计、数控加工的计算等方面的应用范围。

The planar C1 cubic PH splines are constructed , which can be used in the design for the locus of robots and CNC ( Computerized Numerical Control ) interpolating , etc.

本文不同于文献[1]和[2]，采用广义内积定义向量的模，直接对非对称标准特征问题的Lanczos法进行误差分析，得出实用的截断准则。

The accuracy of Lanczos method for non-symmetry standard eigen-problems is analysed in this paper directly by employing generalized inner product to define modulus of vectors , This is different to that in [ 1 ] and [ 2 ] .

在Riemann流形上，证明一条可求长曲线的长度函数等于其切向量的模长函数的Lebesgue积分的充要条件是该曲线绝对连续，从而推广了实分析中的经典结果。

On Riemann manifolds , we prove that for a rectifiable curve , the length function of the curve equals to the Lebesgue integration of the modulus function of its tangent vectors if and only if the curve is absolutely continuous . This generalize a classical result in real analysis .

得到荷载点位置信息后，利用两个向量的模的比例关系来确定荷载的大小。

After getting load point location information , the ratio of vector-mode can be used to determine the amplitude of load .

也就是说，如果朝该方向运动，函数值变动得最剧烈，那么相应的斜率就是梯度向量的模长。

OK , so if I go in that direction , which gives me the fastest increase , then the corresponding slope will be the length of the gradient .

证明了完备、定向曲面的基本群在SU（2）中的表示空间可等同于该曲面上秩为2且具有平凡行列式丛的全纯向量丛的模空间.并且它们具有射影结构。

The representation space of the fundamental group of a closed , oriented Riemannian surface is identified with the moduli space of the holomorphic bundles of rank 2 with trivial determinant bundles over the surface and these spaces are proved to carry a projective structure .

向量空间的模结构分解

Decomposition theorems for vector spaces on module stucture

基于在线支持向量机的非线性内模控制

Nonlinear internal model control based on online support vector machine

只要把这个向量除以它本身的模，得到单位向量。

Well , you take this vector and you scale it down to unit length .

欲求单位法向量，那就用梯度，除以梯度向量的模长。

So , if you wanted a unit normal , that would be the gradient divided by its length .

如果我取一个单位法向量，然后用乘上另一个较长法向量N的模长，会怎样呢？

N What happens if I take a unit normal n and I multiply it by the length of my other normal big N ?

利用向量相等概念，只要已知起点、终点坐标即可求出向量的模，就可推证出两点间的距离公式；

With the concept of vector equality , if coordinates of starting point and terminal point are provided , both mold of vector and distance formula between two points can be worked out .