# Definition The [[Index Notation]] allows us to use the Einstein summation convention, where a sum over the same raised and lowered index is omitted, e.g. the contraction: $ \tilde{\omega}(\pmb{V}) = \sum_j V^j \omega_j \equiv V^j \omega_j $ Other examples include the contractions: $ \begin{align} \tilde{\omega} &= \omega_j \tilde{d}x^j,\\ \pmb{V} &= V^j \frac{\partial}{\partial x^j} \end{align} $