[Edit: change the name of the initial matrix; it should not be Fcvc, it should be S. Add code to construct Fcvc using the 
which we calculate.]
which we calculate.]You can just write a nested for loop (i,j) that does the calculation:
calculation:%Make a 4x4 covariance matrix
N=4; S=eye(N); %identity matrix
for i=1:N,
for j=i+1:N
S(i,j)=-1+2*rand(1,1);
S(j,i)=S(i,j);
end
end
S=10*S %multiply by some arbitray constant
That looks like a reasonable covariance matrix: it is positive along the diagonal, and the absolute value of off-diagonal element are less than the diagoonal, and it is symmetric.
Now compute 
and :
and :siibar=sum(sum(S))/N^2;
sijbar=0;
for i=1:N
for j=i+1:N
sijbar=sijbar+S(i,j);
end
end
sijbar=sijbar/((N^2-N)/2);
fprintf('siibar=%.4f, sijbar=%.4f\n',siibar,sijbar)
Those values look reasonable.
Use siibar and sijbar to make Fcvc
Fcvc=sijbar*(ones(N)-eye(N))+siibar*eye(N)
That looks good.
