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 $$AR=V.$$