import numpy as np

identity = np.eye(2)*0.5
EigVal1, EigVec1 = np.linalg.eig(identity)

print EigVal1
print EigVec1

epsilon = 5e-17 #-5.10313512e-17
identityNoisy = np.array([\
    [0.5,epsilon],\
    [epsilon,0.5]\
    ],dtype=complex)
EigVal2, EigVec2 = np.linalg.eig(identityNoisy)

print EigVal2
print EigVec2