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([[24, 23, 29, 11],
    [ 4,  6,  6, 24],
    [16,  0, 16, 29],
    [27,  1, 19, 27]], order=31)

In [6]: A[:,2] = A[:,1] * GF(17); A
Out[6]: 
GF([[24, 23, 19, 11],
    [ 4,  6,  9, 24],
    [16,  0,  0, 29],
    [27,  1, 17, 27]], 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([[26, 28,  6, 21],
    [15, 28, 26, 25],
    [12,  7, 26,  1],
    [20,  8, 16, 22]], order=31)

In [10]: A[3,:] = A[2,:] * GF(8); A
Out[10]: 
GF([[26, 28,  6, 21],
    [15, 28, 26, 25],
    [12,  7, 26,  1],
    [ 3, 25, 22,  8]], order=31)

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