np.linalg.matrix_power

np.linalg.matrix_power(x)

Raises a square Galois field matrix to an integer power.

References

• https://numpy.org/doc/stable/reference/generated/numpy.linalg.matrix_power.html

Examples

In [1]: GF = galois.GF(31)

In [2]: A = GF.Random((3,3)); A
Out[2]: 
GF([[11,  2,  5],
    [14, 22, 26],
    [29,  3, 19]], order=31)

In [3]: np.linalg.matrix_power(A, 3)
Out[3]: 
GF([[27,  0,  5],
    [20,  3,  7],
    [21, 25, 26]], order=31)

In [4]: A @ A @ A
Out[4]: 
GF([[27,  0,  5],
    [20,  3,  7],
    [21, 25, 26]], order=31)

In [5]: GF = galois.GF(31)

# Ensure A is full rank and invertible
In [6]: while True:
   ...:     A = GF.Random((3,3))
   ...:     if np.linalg.matrix_rank(A) == 3:
   ...:         break
   ...: 

In [7]: A
Out[7]: 
GF([[23, 11,  4],
    [15, 20, 27],
    [29, 23,  4]], order=31)

In [8]: np.linalg.matrix_power(A, -3)
Out[8]: 
GF([[ 2, 21, 25],
    [26, 20, 24],
    [18,  1, 21]], order=31)

In [9]: A_inv = np.linalg.inv(A)

In [10]: A_inv @ A_inv @ A_inv
Out[10]: 
GF([[ 2, 21, 25],
    [26, 20, 24],
    [18,  1, 21]], order=31)