在 LDA 在推导中，说 $w^T\Sigma w$ 代表类内散度，但为什么呢？

import numpy as np import pandas as pd import matplotlib.pyplot as plt 

S = np.array([[1,0],               [0,1]])                mu = np.array([0,0])  s3 = np.random.multivariate_normal(mu,S,500) # generate 1000 samples from the distribution 

# plot the scatter plt.figure(figsize=(10,10))  plt.scatter(s3[:,0],s3[:,1]
       
        ) 
        # set xlim and ylim plt
        .xlim
        (
        -
        10
        ,
        10
        ) plt
        .ylim
        (
        -
        10
        ,
        10
        ) 
        # add grid plt
        .grid
        (
        True
        ) 
        # display the scatter matrix in latex in title plt
        .title
        (
        str
        (S
        [
        0
        ,
        0
        ]
        )
        +
        ' '
        +
        str
        (S
        [
        0
        ,
        1
        ]
        )
        +
        '\n'
        +
        str
        (S
        [
        1
        ,
        0
        ]
        )
        +
        ' '
        +
        str
        (S
        [
        1
        ,
        1
        ]
        )
        ,fontsize
        =
        20
        )