# Definition The standard [[basis]] of $\mathbb{R}^n$ ([[Real Coordinate Space|R^n]]) is the set: $ \begin{align} \pmb{e}_i = \text{0 everywhere except in the $i^\text{th}$ position.} \end{align} $ For example, $ e_3 = (0, 0, 1, 0, 0, \ldots, 0) $ The same set also serves as a basis for $\mathbb{C}^n$ ([[Complex Coordinate Space|C^n]]) (over the field $\mathbb{F} = \mathbb{C}$).