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Real Affine Sets
Real Affine Combinations
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Affine Set Dimensions
Affinely Independent Vectors
Convex Set Dimensions
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Real Affine Hulls


The affine hull of a set in $n$-dimensional space is the intersection of the collection of affine sets which contain it.


We denote the affine hull of $S$ by $\aff S$.

The affine hull of $S \subset \R ^n$ consists of all vectors which can be expressed as

\[ \lambda _1 x_1 + \lambda _2 x_2 \cdots + \lambda _m x_m \]

such that $x_i \in S$ and $\sum_i \lambda _i = 1$.

Also, notice that if $A \subset \R ^n$ is affine, then $\aff A = A$.

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