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([[21, 26, 5], [16, 19, 13], [16, 7, 2]], order=31) In [3]: np.linalg.matrix_power(A, 3) Out[3]: GF([[12, 1, 5], [20, 29, 17], [ 2, 5, 25]], order=31) In [4]: A @ A @ A Out[4]: GF([[12, 1, 5], [20, 29, 17], [ 2, 5, 25]], 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([[28, 5, 19], [16, 6, 11], [12, 10, 23]], order=31) In [8]: np.linalg.matrix_power(A, -3) Out[8]: GF([[18, 0, 5], [ 8, 20, 13], [19, 7, 10]], order=31) In [9]: A_inv = np.linalg.inv(A) In [10]: A_inv @ A_inv @ A_inv Out[10]: GF([[18, 0, 5], [ 8, 20, 13], [19, 7, 10]], order=31)