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function A = hessenberg(A)
n=length(A);

Q=eye(n);
eps=.0000000001;
s=0;
countwhile=0;

for i=1:1:n-2
    
    %while is step b)
    while(s<=eps)
    
        %step a)
        s=0;
        for j=i+countwhile+1:1:n
            s=s+A(j,i+countwhile)^2; 
        end
        s=sqrt(s);

        rho=-sign(A(i+1+countwhile,i+countwhile));
        c=sqrt(2*s*(s+abs(A(i+1+countwhile,i+countwhile))));

        countwhile=countwhile+1;        
    end
    
    %step c)
    Q(i+1,i)=(A(i+1,i)-rho*s)/c;
    for j=i+2:1:n
        Q(j,i)=A(j,i)/c;
        
    end
    
    %step d)
    A(i+1,i)=rho*s;
    for j=i+2:1:n
        A(j,i)=0;        
    end
    
    %step e)
    for j=1:1:i
        s=0;
        for k=i+1:1:n
            s=s+Q(k,i)*A(j,k);
        end
        s=2*s;        
        for k=i+1:1:n
            A(j,k)=A(j,k)-s*Q(k,i);            
        end        
    end
    
    %step f)
    for j=1:1:i
        s=0;
        for k=i+1:1:n
            s=s+Q(k,i)*A(k,j);            
        end
        s=2*s;
        for k=i+1:1:n
            A(k,j)=A(k,j)-s*Q(k,i);            
        end        
    end
    
    %step g)
    s=0;
    for j=i+1:1:n
        s=s+Q(k,i)*A(j,k);
    end
    s=2*s;
    
    for j=i+1:1:n
        A(j,k)=A(j,k)-s*Q(k,i);        
    end   
    s=0;
end

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 %step g)   
    for j=i+1:1:n
        s=2*(Q(i+1:n,i)'*A(j,i+1:n)');
    
    for k=i+1:1:n
        A(j,k)=A(j,k)-s*Q(k,i);        
    end
    end