np.linalg.matrix_power
- np.linalg.matrix_power(x)
Raises a square Galois field matrix to an integer power.
References
Examples
In [1]: GF = galois.GF(31) In [2]: A = GF.Random((3,3)); A Out[2]: GF([[25, 6, 6], [29, 24, 10], [17, 21, 29]], order=31) In [3]: np.linalg.matrix_power(A, 3) Out[3]: GF([[ 3, 21, 3], [ 6, 2, 6], [11, 8, 3]], order=31) In [4]: A @ A @ A Out[4]: GF([[ 3, 21, 3], [ 6, 2, 6], [11, 8, 3]], 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([[25, 25, 23], [25, 30, 14], [10, 8, 15]], order=31) In [8]: np.linalg.matrix_power(A, -3) Out[8]: GF([[ 3, 26, 11], [23, 3, 14], [ 4, 27, 15]], order=31) In [9]: A_inv = np.linalg.inv(A) In [10]: A_inv @ A_inv @ A_inv Out[10]: GF([[ 3, 26, 11], [23, 3, 14], [ 4, 27, 15]], order=31)