import numpy as np
import numpy.linalg as alg

def matrice(a,b):
    M=np.array([[1,-a,-a,1],
               [1-b,a,a-1,-b],
               [b,-a,1-a,1+b],
               [0,a,a,0]])
    return M

def propre(a,b):
    return alg.eig(matrice(a,b))


print(matrice(1,2))
print(propre(1,2)[0])
print(propre(1,2)[1])

A=matrice(1,2)
B=matrice(1,2)-np.eye(4)
print(A.dot(B).dot(B))
print(A.dot(A).dot(B))
print(A.dot(A).dot(B).dot(B))