np.linalg.matrix_power¶

np.linalg.matrix_power(x)[source]¶

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([[ 2, 16,  8],
    [11, 21, 20],
    [25,  6, 14]], order=31)

In [3]: np.linalg.matrix_power(A, 3)
Out[3]: 
GF([[13, 20, 24],
    [18, 13, 21],
    [20, 19, 26]], order=31)

In [4]: A @ A @ A
Out[4]: 
GF([[13, 20, 24],
    [18, 13, 21],
    [20, 19, 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([[ 3, 10, 18],
    [20, 14, 18],
    [14, 26,  5]], order=31)

In [8]: np.linalg.matrix_power(A, -3)
Out[8]: 
GF([[13, 27,  6],
    [15, 10, 30],
    [16,  1, 24]], order=31)

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

In [10]: A_inv @ A_inv @ A_inv
Out[10]: 
GF([[13, 27,  6],
    [15, 10, 30],
    [16,  1, 24]], order=31)