Compute rank of matrix over Galois field
rk = gfrank(A,p)
Note: This function performs computations in GF(pm) where p is prime. If you are working in GF(2m), use the rank function with Galois arrays. For details, see Computing Ranks.
rk = gfrank(A,p) calculates the rank of the matrix A in GF(p), where p is a prime number.
In the code below, gfrank says that the matrix A has less than full rank. This conclusion makes sense because the determinant of A is zero mod p.
A = [1 0 1; 2 1 0; 0 1 1]; p = 3; det_a = det(A); % Ordinary determinant of A detmodp = rem(det(A),p); % Determinant mod p rankp = gfrank(A,p); disp(['Determinant = ',num2str(det_a)]) disp(['Determinant mod p is ',num2str(detmodp)]) disp(['Rank over GF(p) is ',num2str(rankp)])
The output is below.
Determinant = 3 Determinant mod p is 0 Rank over GF(p) is 2