np.linalg.matrix_rank

np.linalg.matrix_rank(x)

Returns the rank of a Galois field matrix.

References

• https://numpy.org/doc/stable/reference/generated/numpy.linalg.matrix_rank.html

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([[16,  8,  2, 12],
    [29, 17, 12, 16],
    [18, 19, 25, 27],
    [ 4,  7, 15, 10]], order=31)

In [6]: A[:,2] = A[:,1] * GF(17); A
Out[6]: 
GF([[16,  8, 12, 12],
    [29, 17, 10, 16],
    [18, 19, 13, 27],
    [ 4,  7, 26, 10]], 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, 23, 23, 18],
    [11, 18,  8,  0],
    [25, 17, 30, 18],
    [14, 19, 11,  7]], order=31)

In [10]: A[3,:] = A[2,:] * GF(8); A
Out[10]: 
GF([[14, 23, 23, 18],
    [11, 18,  8,  0],
    [25, 17, 30, 18],
    [14, 12, 23, 20]], order=31)

In [11]: np.linalg.matrix_rank(A)
Out[11]: 3