np.linalg.matrix_rank
- np.linalg.matrix_rank(x)
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([[19, 18, 19, 10], [29, 13, 22, 11], [ 3, 21, 22, 0], [15, 20, 22, 13]], order=31) In [6]: A[:,2] = A[:,1] * GF(17); A Out[6]: GF([[19, 18, 27, 10], [29, 13, 4, 11], [ 3, 21, 16, 0], [15, 20, 30, 13]], 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([[14, 22, 16, 27], [28, 15, 24, 22], [ 2, 4, 30, 14], [10, 20, 24, 12]], order=31) In [10]: A[3,:] = A[2,:] * GF(8); A Out[10]: GF([[14, 22, 16, 27], [28, 15, 24, 22], [ 2, 4, 30, 14], [16, 1, 23, 19]], order=31) In [11]: np.linalg.matrix_rank(A) Out[11]: 3