The first task is then to set up the matrix \( A \) for a given \( k_0 \). This is an \( (N+1)\times (N+1) \) matrix. It can be convenient to have an outer loop which runs over the chosen observable values for the energy \( k_0^2/m \). {\em Note that all mesh points \( k_j \) for \( j=1,N \) must be different from \( k_0 \). Note also that \( V(k_i,k_j) \) is an \( (N+1)\times (N+1) \) matrix}.

With the matrix \( A \) we can rewrite the problem as a matrix problem of dimension \( (N+1)\times (N+1) \). All matrices \( R \), \( A \) and \( V \) have this dimension and we get $$ A_{i,l}R_{l,j}=V_{i,j}, $$ or just $$ AR=V. $$