import scipy as np
from scipy import linalg
a=np.matrix([[1,2],[2,1]])
e=np.linalg.eig(a)
print(np.dot(np.dot(e[1], np.diag(e[0])), e[1].T)) #ok
print(np.dot(np.dot(e[1], np.matrix([[4,3],[3,4]])), e[1].T))
print(np.dot(e[1], np.dot(np.matrix([[4,3],[3,4]]), e[1].T)))# not ok
print(np.dot(e[1], e[1].T))# ok
print(np.dot(e[1].T, e[1]))# ok
print(np.dot(e[1].T, np.dot(a, e[1])))# not ok