np.linalg.matrix_rank¶

np.linalg.matrix_rank(x)[source]¶

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.Eye(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([[ 5, 23, 28, 20],
    [13,  3,  7, 30],
    [10, 27,  2, 20],
    [10,  5,  5,  4]], order=31)

In [6]: A[:,2] = A[:,1] * GF(17); A
Out[6]: 
GF([[ 5, 23, 19, 20],
    [13,  3, 20, 30],
    [10, 27, 25, 20],
    [10,  5, 23,  4]], 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, 19, 13, 11],
    [28, 11, 27, 20],
    [10, 12, 25,  3],
    [16, 16, 17, 21]], order=31)

In [10]: A[3,:] = A[2,:] * GF(8); A
Out[10]: 
GF([[26, 19, 13, 11],
    [28, 11, 27, 20],
    [10, 12, 25,  3],
    [18,  3, 14, 24]], order=31)

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