= Conic Carathéodory theorem
In an $N$-dimensional real <vector space>, each member of a <conic hull> has a representation using at most $N$ generators. To prove it, take a finite positive-coefficient representation with more than $N$ terms. Its generators are linearly dependent, say $\sum_j\mu_js_j=0$, with some $\mu_j>0$ after reversing the relation if necessary. Subtract $t\mu_j$ from each <coefficient>, taking $t=\min_{\mu_j>0}\lambda_j/\mu_j$. All <coefficients> stay nonnegative and at least one vanishes. Iterate. The bound differs from the $N+1$ bound for a <convex hull> because the <coefficient> sum is unrestricted.
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