Is the way I simplify my notation?

Question

Do you agree with how I simplify this equation notation

$$\sum_{i=1}^n \phi_{v_i} \left(\sum_{i=1}^m \phi_{l_i}\right)=\sum_{(i,j)\in \mathcal{S}}\phi_{v_i}\phi_{l_j},$$

where I define $$\mathcal{S}=\{(i,j):i\in[1:n], j\in [1:m] \}?$$

Thanks

Answer 1

That's totally fine. I might think it is more commonly written as $$ \sum_{\substack{ 1 \leq i \leq n \\ 1 \leq j \leq m}} \phi_{v_i}\,\phi_{l_j},$$ or if the ranges of summation are clear, then $$ \sum_{i,\,j} \phi_{v_i}\,\phi_{l_j}.$$