Why we need affine independent to ensure the unique representation of a vector from convex hull. As far as I understood, the converse of the theorem is not true. In other words, if any vector is in the convex hull of $\mathbb{M}$, can be written as a unique convex combination of the vectors in $\mathbb{M}$, then can we say the vectors in $\mathbb{M}$ are affinely independent? What can be a counterexample?
2026-03-26 13:51:08.1774533068
Does unique convex combination imply affine independence?
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