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([[ 4,  0,  3,  4],
    [14, 28, 19, 16],
    [ 8, 21, 26, 20],
    [ 0, 17, 12,  2]], order=31)

In [6]: A[:,2] = A[:,1] * GF(17); A
Out[6]: 
GF([[ 4,  0,  0,  4],
    [14, 28, 11, 16],
    [ 8, 21, 16, 20],
    [ 0, 17, 10,  2]], 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([[19,  6,  3,  6],
    [ 5, 23, 28,  4],
    [25, 11, 20, 27],
    [18,  6,  0, 12]], order=31)

In [10]: A[3,:] = A[2,:] * GF(8); A
Out[10]: 
GF([[19,  6,  3,  6],
    [ 5, 23, 28,  4],
    [25, 11, 20, 27],
    [14, 26,  5, 30]], order=31)

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