点积，余弦定理，复共轭

点积：在数学中，数量积（dot product; scalar product，也称为点积）是接受在实数R上的两个向量并返回一个实数值标量的二元运算。它是欧几里得空间的标准内积。

http://baike.baidu.com/link?url=jVfGaAWPAfzatZsQuAztJKPJKJCGbzlMrwiFCNc6i-f4RfQatXL5JGz5IZmGJlQSJu0ReW3y89jmdQYqJkLlA8FxZsqFy-3TtKbNZdf5FngLOl0HM8jClkA5u6_GzKIMyQbVgU5jfLw1QokOGLtJjz9g566dNAhUTBGbV4m4FHi

两个向量a = [a1, a2,…, an]和b = [b1, b2,…, bn]的点积定义为：

a·b=a1b1+a2b2+……+anbn。

使用矩阵乘法并把（纵列）向量当作n×1 矩阵，点积还可以写为：

a·b=a*b^T，这里的b^T指示矩阵b的转置。

设A为 m x p 的矩阵，B为 p x n 的矩阵，那么称 m x n 的矩阵C为矩阵A与B的乘积，记作 C = AB ，其中矩阵中的第 i 行第 j 列元素可以表示为：

例子：

In [1]: import numpy as np

In [2]: a = 2

In [3]: b = 3

In [4]: np.dot(a,b)
Out[4]: 6

In [5]: a = [3, 4]

In [6]: b = [5, 6]

In [7]: np.dot(a,b)
Out[7]: 39

In [8]: a = [[1,2],[3,4]]

In [9]: b = [[1,2],[2,3],[3,4]]

In [10]: np.dot(a,b)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-10-71281829ef00> in <module>()
----> 1 np.dot(a,b)

ValueError: shapes (2,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)

In [11]: np.dot(b,a)
Out[11]: 
array([[ 7, 10],
 [11, 16],
 [15, 22]])

In [1]: import numpy as np

In [2]: a = 2

In [3]: b = 3

In [4]: np.dot(a,b)

Out[4]: 6

In [5]: a = [3, 4]

In [6]: b = [5, 6]

In [7]: np.dot(a,b)

Out[7]: 39

In [8]: a = [[1,2],[3,4]]

In [9]: b = [[1,2],[2,3],[3,4]]

In [10]: np.dot(a,b)

---------------------------------------------------------------------------

ValueError Traceback (most recent call last)

<ipython-input-10-71281829ef00> in <module>()

----> 1 np.dot(a,b)

ValueError: shapes (2,2) and (3,2) not aligned: 2 (dim 1) != 3 (dim 0)

In [11]: np.dot(b,a)

Out[11]:

array([[ 7, 10],

[11, 16],

[15, 22]])

余弦定理(The Law of Cosines)：

http://baike.baidu.com/item/%E4%BD%99%E5%BC%A6%E5%AE%9A%E7%90%86#2_1

复共轭（complex conjugate):

https://en.wikipedia.org/wiki/Complex_conjugate

Geometric representation of z and its conjugate z̅ in the complex plane. The complex conjugate is found by reflecting z across the real axis.

In mathematics, the complex conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign.^[1]^[2] For example, the complex conjugate of 3 + 4i is 3 − 4i.

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