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, 11, 16], [12, 30, 6], [ 3, 24, 8]], order=31) In [3]: np.linalg.matrix_power(A, 3) Out[3]: GF([[16, 19, 6], [20, 25, 29], [21, 1, 22]], order=31) In [4]: A @ A @ A Out[4]: GF([[16, 19, 6], [20, 25, 29], [21, 1, 22]], 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([[17, 28, 14], [ 4, 22, 9], [27, 21, 24]], order=31) In [8]: np.linalg.matrix_power(A, -3) Out[8]: GF([[27, 0, 1], [12, 26, 1], [20, 19, 10]], order=31) In [9]: A_inv = np.linalg.inv(A) In [10]: A_inv @ A_inv @ A_inv Out[10]: GF([[27, 0, 1], [12, 26, 1], [20, 19, 10]], order=31)