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([[ 7,  5,  1, 21],
    [ 3, 12, 16,  8],
    [15, 16, 23,  2],
    [10,  9,  8,  9]], order=31)

In [6]: A[:,2] = A[:,1] * GF(17); A
Out[6]: 
GF([[ 7,  5, 23, 21],
    [ 3, 12, 18,  8],
    [15, 16, 24,  2],
    [10,  9, 29,  9]], 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([[ 3, 24,  9, 10],
    [14, 23, 20, 24],
    [29,  3, 28, 14],
    [ 4,  5, 10, 10]], order=31)

In [10]: A[3,:] = A[2,:] * GF(8); A
Out[10]: 
GF([[ 3, 24,  9, 10],
    [14, 23, 20, 24],
    [29,  3, 28, 14],
    [15, 24,  7, 19]], order=31)

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