E = [1 1 1 1; 3 1 2 1; 1 2 4 8]
C = [1 2 3 1; 0 1 2 1; 2 1 0 -1]
m1 = size(E, 1)
n1 = size(E, 2)
K = kernel(C)
k = size(K, 2)
L = kernel(K')
M = E * K
N = kernel(M')
P = [K L(:,1:m1-k)]
R = clean(P * inv([M N]))
S = [eye(n1,n1)-R*E; C]
rank(S)