function A = AllRanks(k) 
      
% Creates matrices A(1), A(2), ..., A((k^2+1)/2) of size k^2-by-k^2
% and all possible ranks satisfying A^2 = J by a series of switches
% starting with the standard form.
 
if (k < 2) return; end 
A(:,:,1) = MakeStandard(k); 
 
for i=1:k-2 
    V(i,1) = i+1; 
    V(i,2) = i+2;
    V(i,3) = (k+1)*i+2; 
    V(i,4) = (k+1)*i+2+k;
end 
for i=1:k-3 
    for j=1:i 
       m=(i*(i-1))/2+j;
       if j==1 
          V(m+k-2,1)=(i+2)*k+2; 
          V(m+k-2,2)=(i+2)*(k+1); 
       else
          V(m+k-2,1)=(i+2)*k+j;
          V(m+k-2,2)=(i+2)*k+j+1;
       end
       V(m+k-2,3)=j*k+i+3;
       V(m+k-2,4)=(i+1)*k+i+3;
    end 
end 
p = k-2+((k-3)*(k-2))/2; 
for i=1:floor((k-1)/2)
    V(p+i,1) = 2*i*k+1;
    V(p+i,2) = 2*i*(k+1);
    V(p+i,3) = 1; 
    V(p+i,4) = (2*(i-1)+1)*k+1;
end 
           
if (k <= 2) return; end
           
[x y] = size(V); 
for i = 1:x
    A(:,:,i+1) = MakeSwitch(V(i,1),V(i,2),V(i,3),V(i,4),A(:,:,i));
end