We have $$S=S_{ij}l_il_j$$ where $l_i$ is a unit vector in the direction in which $S$ is evaluated.
If we want to evaluate $S$ in the direction of the vector $a_i$ we would calculate $$S=\frac{S_{ij}a_ia_j}{|a_i|^2}=S_{ij}\hat a_i \hat a_j$$
If we want to evaluate $S$ in the direction of a differently oriented vector $b_i$ we would calculate $$S=\frac{S_{ij}b_ib_j}{|b_i|^2}=S_{ij}\hat b_i \hat b_j$$
How should one notate these two values of $S$ to distinguish them? E.g., would the notation $S(a_i)$ and $S(b_i)$ be valid? What has been used in literature?