# General Usage Components of [[vector|vectors]] have the index written as a superscript, e.g. $V^i$, while components of [[one-form|one-forms]] have their indices written as subscripts, e.g. $q_j$. The [[basis|bases]] follow the opposite convention, members of a vector basis are labeled by a subscript $\{e_i\}$ while members of a one-form basis are written with a superscript $\{\tilde{\omega}^j\}$. For [[Coordinate Chart|coordinate]] bases, one-forms have their index up, as they should (e.g. $\tilde{d}x^j$), while vectors have (e.g. $\partial/\partial x^i$) are considered to have their index down since it is in the denominator. These conventions are adopted for a good reason. They allow us to use the [[einstein summation convention]]. # Special Relativity We can raise and lower indices using the [[Minkowski Metric]] $ \begin{align} v^\nu &= v_{\mu}\eta^{\mu\nu}, \\ v_\nu &= v^{\mu}\eta_{\mu\nu} \end{align} $ The latter are the components of the dual vector, and the former are the components of the vector.