伴随每个递归步骤，会形成带有一个额外置换群的向量积。
With each recursive step, cross products with one additional Permutation Group are formed.
角动量：(有参照点)的矢量和粒子线性动量的向量积。
Angular momentum: the vector product of the position vector (from a reference point) and the linear momentum of a particle.
一旦你得到一个这样的计算式，你对向量场做点积，这和前面这个不一样。
Once you have such a formula, you do the dot product with this vector field, which is not the same as that one.
我们来看它的第一个意义，在我们用两个，不一样的向量相乘之前，我们先看一个向量和它本身的点积。
Well, the first thing it means before we multiply two vectors, let's start multiplying a vector with itself That's probably easier.
第一单元学得叉积、法向量这些,现在就有用了。
The first unit about cross-products,normal vectors and so on is actually useful now.
为了找到带法向量的面元，我就取这两个的叉积。
To find the surface element together with a normal vector, I would just take the cross-product between these guys.
我将要证明，一个只有z分量的向量场的通量,等于一个三重积分，其中被积表达式为。
I'm going to prove that the flux of a vector field that has only a z component is actually equal to the triple integral of, RzdV well, the divergence of this is just R sub z dV.
可以把这些用向量形式重新写下来，就是梯度向量和位置改变量的点积。
And I can rewrite this in vector form as the gradient dot product the amount by which the position vector has changed.
我们要做的是，沿着曲线的每一点上，取向量场和法向量的点积。
What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.
这是平面法向量，和沿直线向量的点积。
It's the dot product between the normal vector of a plane and the vector along the line.
如何将一个元组向量为向量元组使用笛卡尔积？
How to convert a tuple of vectors into a vector of tuples using the Cartesian product?
本文首先研究了一类积集上的广义向量拟类变分不等式问题，使用不动点定理给出了它的解的存在性结果。
In this thesis, first, we employ the fixed point theorem to establish the existence of solution of a class of generalized vector quasi-variational-like inequality over product sets.
运用输入输出轴两轴线的向量叉积求出了联轴器夹角方程序。
And then, the expression of the fluctuation of the joint Angle was derived from the cross product of the centerlines of the input and output shafts.
第一章是向量代数，主要介绍向量的线性运算、向量的内积、向量的外积、向量的混合积和双重外积。
The first chapter is about vector algebra, introduces the vector of linear operations, inner product of vectors, vector outer product, vector product and double mixed exterior product.
该方法首先对地球物理和地球化学等网格数据进行二维矩阵的奇异值分解，之后用左特征向量矩阵与右特征向量矩阵的直积构造一个正交完备基。
The MSVD method constructs a self-contained orthogonal basis using the outer product of left and right eigenvector matrixes decomposed from 2D geochemical or geophysical maps.
矢量积节点计算两个向量的数目积。
The Vector Product node computes the Dot Product of two vectors.
Drawa UMLdiagram first编写和测试vector2d定义加法，减法，数量积，输入和输出操作符一类，和两个二维向量的内积。
Write and test a class Vector2D to define operators for addition, subtraction, scalar product, input and output, and inner product of two 2d vectors.
Drawa UMLdiagram first编写和测试vector2d定义加法，减法，数量积，输入和输出操作符一类，和两个二维向量的内积。
Write and test a class Vector2D to define operators for addition, subtraction, scalar product, input and output, and inner product of two 2d vectors.
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