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([[21,  5,  9],
    [13,  0, 14],
    [28, 17, 14]], order=31)

In [3]: np.linalg.matrix_power(A, 3)
Out[3]: 
GF([[13, 12, 14],
    [ 8, 28,  8],
    [22, 28,  6]], order=31)

In [4]: A @ A @ A
Out[4]: 
GF([[13, 12, 14],
    [ 8, 28,  8],
    [22, 28,  6]], 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([[26, 12, 30],
    [10,  7, 23],
    [ 1, 15, 22]], order=31)

In [8]: np.linalg.matrix_power(A, -3)
Out[8]: 
GF([[ 4, 30,  1],
    [27,  5,  6],
    [23,  9, 10]], order=31)

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

In [10]: A_inv @ A_inv @ A_inv
Out[10]: 
GF([[ 4, 30,  1],
    [27,  5,  6],
    [23,  9, 10]], order=31)