I came across this definition of a tensor while reading some vector calculus literature
This definition contains the index $\ell$ in the last term, however the tensor itself only depends on $j$ and $k$. What am I supposed to do with this extra index? Do I sum over it?
Note: The term $\frac{\partial \phi_k}{\partial x_j}$ is irrelevant here; it is just another long expression in terms of the position vectors, although it also contains an $\ell$ within it.