In [1]:

    

import numpy as np


    

In [2]:

    

arr = np.array([[8, 1], [4, 5]])


    

In [3]:

    

w, v = np.linalg.eig(arr)


    

In [4]:

    

print(w)


    

    




[9. 4.]

In [5]:

    

print(v)


    

    




[[ 0.70710678 -0.24253563]
 [ 0.70710678  0.9701425 ]]

In [6]:

    

print('value: ', w[0])
print('vector: ', v[:, 0] / v[0, 0])


    

    




value:  9.0
vector:  [1. 1.]

In [7]:

    

print(w[np.argmax(w)])
print(v[:, np.argmax(w)])


    

    




9.0
[0.70710678 0.70710678]

In [8]:

    

def get_eigenpairs(arr):
    w, v = np.linalg.eig(arr)
    eigenpairs = []
    
    for i, val in enumerate(w):
        vec = v[:, i] / np.min(np.abs(v[:, i][v[:, i] != 0]))
        eigenpairs.append((val, vec))
        
    return eigenpairs


    

In [9]:

    

eigenpairs = get_eigenpairs(arr)

for val, vec in eigenpairs:
    print('value: {}, vector: {}'.format(val, vec))


    

    




value: 9.0, vector: [1. 1.]
value: 4.0, vector: [-1.  4.]

In [10]:

    

arr = np.array([[1, 1, 2], [0, 2, -1], [0, 0, 3]])

eigenpairs = get_eigenpairs(arr)

for val, vec in eigenpairs:
    print('value: {}, vector: {}'.format(val, vec))


    

    




value: 1.0, vector: [1. 0. 0.]
value: 2.0, vector: [1. 1. 0.]
value: 3.0, vector: [ 1. -2.  2.]

In [11]:

    

arr = np.array([[3, 2], [-2, 3]])

eigenpairs = get_eigenpairs(arr)

for val, vec in eigenpairs:
    print('value: {}, vector: {}'.format(val, vec))


    

    




value: (3+2.0000000000000004j), vector: [0.-1.j 1.+0.j]
value: (3-2.0000000000000004j), vector: [0.+1.j 1.-0.j]