\begin{definition}[Definition:Coordinate System/Coordinates on Affine Space]
Let $\EE$ be an affine space of dimension $n$ over a field $k$.
Let $\RR = \tuple {p_0, e_1, \ldots, e_n}$ be an affine frame in $\EE$.
Let $p \in \EE$ be a point.
Since Affine Coordinates are Well-Defined, there exists a unique ordered tuple $\tuple {\lambda_1, \ldots, \lambda_n} \in k^n$ such that:
:$\ds p = p_0 + \sum_{i \mathop = 1}^n \lambda_i e_i$
The numbers $\lambda_1, \ldots, \lambda_n$ are the '''coordinates''' of $p$ in the frame $\RR$.
Category:Definitions/Affine Geometry
\end{definition}