Hessenberg matrix

Question

Modify the factorization algorithm $LU$ to efficiently factorize a Hessenberg matrix where factorization algorithm $LU$ is

function [A] = lu_kji (A)

    [n,n]=size(A);

    for k=1:n-1
        A(k+1:n,k)=A(k+1:n,k)/A(k,k);
        for j=k+1:n
            for i=k+1:n
                A(i,j)=A(i,j)-A(i,k)*A(k,j);
            end
        end
    end
end

Help me please whit HINT, thanks for your helping me.