I want to express that I loop over k vectors $s_1 \dots s_k$ and so some calculation with them in function f. The output of f is a scalar, and together these k values form a new vector a. I want to show in the formula that we do this for k steps, as this is important for the reader to understand.
For a summation, we would normally write this:
$a = \sum_{i=1}^k f(s_i)$
But the output shouldn't be a sum, but a vector. What is the correct notation here? Is there simply a symbol I can use instead of the summation symbol, or do I have to rewrite the formula?
Best Answer
You can define $\mathbf{a}$ by (I use bold font here to indicate the vectors):
$$\mathbf{a} = (a_1, \ldots, a_k),$$
where $a_i = f(\mathbf{s_i})$ for $i = 1, \dots, k$.
In a shorter form:
$$\mathbf{a} = (f(\mathbf{s_1}), \ldots, f(\mathbf{s_k})).$$