###### tags:`other`

import numpy as np

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

np.linalg.matrix_power(mat_cycle, 1)
np.linalg.matrix_power(mat_cycle, 2)
np.linalg.matrix_power(mat_cycle, 3)
np.linalg.matrix_power(mat_cycle, 4)
np.linalg.matrix_power(mat_cycle, 5)

array([[0, 0, 1, 0],
       [0, 0, 0, 1],
       [0, 1, 0, 0],
       [1, 0, 0, 0]])

array([[0, 1, 0, 0],
       [1, 0, 0, 0],
       [0, 0, 0, 1],
       [0, 0, 1, 0]])

array([[0, 0, 0, 1],
       [0, 0, 1, 0],
       [1, 0, 0, 0],
       [0, 1, 0, 0]])

array([[1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 0, 1]])

array([[0, 0, 1, 0],
       [0, 0, 0, 1],
       [0, 1, 0, 0],
       [1, 0, 0, 0]])