Definition:Coordinate System/Coordinates on Affine Space
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Definition
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 $\RR$.