Geometric independence

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Definition

Let us have a set of points, $\{a_0,a_1,\ldots,a_N\}\subseteq\mathbb{R}^n$, we say they are geometrically independent if:

• $$\forall \{t_0,t_1,\ldots,t_N\}\subset\mathbb{R}\left[\left(\sum^N_{i=1}t_i=0\wedge\sum^N_{i=1}t_ia_i=0\right)\implies\left(t_0=t_1=\ldots=t_N=0\right)\right]$$

The reader should note that this is very similar to linear independence; in fact, $\{a_0,\ldots,a_N\}$ is geometrically independent iff the set $\{a_1-a_0,\ldots,a_N-a_0\}$ is linearly independent

References

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TODO: Is this in the right category?

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