Incorrect EigenValues/Vectors with Numpy

Question

I am trying to find the eigenvalues/vectors for the following matrix:

A = np.array([[1, 0, 0],
              [0, 1, 0],
              [1, 1, 0]])


        

Answer 1

The eigenvalues returned by linalg.eig are columns vectors, so you need to iterate over the transpose of e_vecs (since iteration over a 2D array returns row vectors by default):

import numpy as np
import numpy.linalg as LA
A = np.array([[1, 0, 0], [0, 1, 0], [1, 1, 0]])
e_vals, e_vecs = LA.eig(A)

print(e_vals)
# [ 0.  1.  1.]
print(e_vecs)
# [[ 0.          0.          1.        ]
#  [ 0.70710678  0.          0.70710678]
#  [ 0.          0.70710678  0.70710678]]

for val, vec in zip(e_vals, e_vecs.T):
    assert np.allclose(np.dot(A, vec), val * vec)