Math Help - Suffix Notation Operators

1. Suffix Notation Operators

A very quick question here, going over my lectures notes and I've missed out an example on suffix notation, I've got

1) $(\nabla \phi)_i = \frac{\partial \phi}{\partial x_i}$
...
7) $\left[ (\upsilon \cdot \nabla) u \right]_i =$

I included the first one as an example of the new notation they were giving us examples of, and 7) is the one I've got missing, would be grateful if someone could help me out.

Thanks in advance.

2. Well, you could use Einstein summation notation for the dot product there. I would use a summed variable for the dot product that is not i, or it'll get confusing. Can you continue?