# Definition Given a set of arbitrary [[basis]] [[Vector Field|vector fields]], if the [[Commutator]] of two of them, e.g., $\pmb{V} = \frac{d}{d\lambda}$ and $\pmb{W} = \frac{d}{d\mu}$ does not vanish, then they are known form a *non-coordinate basis* and they cannot be written in terms of the derivatives of [[coordinate basis|coordinates]].