Difference between Hadamard product and matrix product in python

Let's briefly talk about Hadamard product: 
 
(refer to Wikipedia: https://en.wikipedia.org/wiki/Hadamard_product_(matrices) ) 
and matrix product is: 
 
(refer to Wikipedia: matrix product ) 
The two are completely different , but why python is represented by ∗ ∗? By consulting the official documentation ( PEP465 ), we can get the following explanation: 
For numpy.ndarray objects, * performs elementwise multiplication, and matrix multiplication must use a function call (numpy.dot). For numpy.matrix objects, * performs matrix multiplication, and elementwise multiplication requires function syntax. 
That is, when the variable type is numpy.ndarray, ∗ represents the Hadamard product; when the variable type is numpy.matrix, ∗ represents the matrix product. The variable type in the LSTM source code is numpy.ndarray, so use ∗The operation naturally represents the Hadamard product, and the problem is solved. 
Here's a simple example to distinguish between these two operations:

## Hadamard product
import numpy as np
a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
a * b
Out[5]:
array([[ 5, 12],
       [21, 32]])

## matrix product
c = np.matrix(a)
d = np.matrix(b)
c * d
Out[8]:
matrix([[19, 22],
        [43, 50]])

　　

It can be seen that the results obtained by the same * operation are different because the variable types are different. 
Of course, a variable whose variable type is numpy.array can also perform matrix multiplication through the numpy.dot() function:

np.dot(a,b)
Out[9]:
array([[19, 22],
       [43, 50]])

　　

参考：https://blog.csdn.net/flying_sfeng/article/details/79330336