In [2]:

    

import numpy as np


    

In [23]:

    

cov = np.array([[5, -3, 0],[-3, 5, 0],[0, 0, 4]])
cov


    

    
Out[23]:





array([[ 5, -3,  0],
       [-3,  5,  0],
       [ 0,  0,  4]])

In [24]:

    

evals, evecs = np.linalg.eig(cov)


    

In [25]:

    

evals


    

    
Out[25]:





array([ 8.,  2.,  4.])

In [26]:

    

evecs


    

    
Out[26]:





array([[ 0.70710678,  0.70710678,  0.        ],
       [-0.70710678,  0.70710678,  0.        ],
       [ 0.        ,  0.        ,  1.        ]])

In [84]:

    

x=np.array([[4,0,2]])
x


    

    
Out[84]:





array([[4, 0, 2]])

In [85]:

    

components = np.array([evecs[:,0], evecs[:,2]]).T #these are the 2 vecs w/ most variance
U = components
U


    

    
Out[85]:





array([[ 0.70710678,  0.        ],
       [-0.70710678,  0.        ],
       [ 0.        ,  1.        ]])

In [86]:

    

x2d = np.dot(U.T,x.T).T
x2d


    

    
Out[86]:





array([[ 2.82842712,  2.        ]])

In [87]:

    

UUT = np.dot(U,U.T)
UUT


    

    
Out[87]:





array([[ 0.5, -0.5,  0. ],
       [-0.5,  0.5,  0. ],
       [ 0. ,  0. ,  1. ]])

In [89]:

    

x3d = np.dot(UUT, x.T)
x3d.T


    

    
Out[89]:





array([[ 2., -2.,  2.]])