np.linalg.matrix_rank¶
- np.linalg.matrix_rank(x)[source]¶
Returns the rank of a Galois field matrix.
References
Examples
In [1]: GF = galois.GF(31) In [2]: A = GF.Identity(4); A Out[2]: GF([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], order=31) In [3]: np.linalg.matrix_rank(A) Out[3]: 4
One column is a linear combination of another.
In [4]: GF = galois.GF(31) In [5]: A = GF.Random((4,4)); A Out[5]: GF([[15, 5, 4, 10], [ 0, 24, 24, 4], [ 1, 9, 24, 1], [ 6, 22, 0, 29]], order=31) In [6]: A[:,2] = A[:,1] * GF(17); A Out[6]: GF([[15, 5, 23, 10], [ 0, 24, 5, 4], [ 1, 9, 29, 1], [ 6, 22, 2, 29]], order=31) In [7]: np.linalg.matrix_rank(A) Out[7]: 3
One row is a linear combination of another.
In [8]: GF = galois.GF(31) In [9]: A = GF.Random((4,4)); A Out[9]: GF([[ 1, 8, 20, 18], [21, 6, 26, 12], [13, 3, 20, 15], [17, 15, 6, 29]], order=31) In [10]: A[3,:] = A[2,:] * GF(8); A Out[10]: GF([[ 1, 8, 20, 18], [21, 6, 26, 12], [13, 3, 20, 15], [11, 24, 5, 27]], order=31) In [11]: np.linalg.matrix_rank(A) Out[11]: 3