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([[12, 26,  0],
    [18,  6,  7],
    [ 0, 28,  4]], order=31)

In [3]: np.linalg.matrix_power(A, 3)
Out[3]: 
GF([[20,  8,  5],
    [27, 14,  3],
    [21, 12, 18]], order=31)

In [4]: A @ A @ A
Out[4]: 
GF([[20,  8,  5],
    [27, 14,  3],
    [21, 12, 18]], 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([[30, 18, 20],
    [ 6, 15, 27],
    [ 3,  6, 21]], order=31)

In [8]: np.linalg.matrix_power(A, -3)
Out[8]: 
GF([[10, 26,  6],
    [17, 12, 19],
    [12, 27, 16]], order=31)

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

In [10]: A_inv @ A_inv @ A_inv
Out[10]: 
GF([[10, 26,  6],
    [17, 12, 19],
    [12, 27, 16]], order=31)