Definition:Convex Hull

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Let $X$ be a vector space over $\R$.

Let $U \subseteq X$.

We define the convex hull of $U$, written $\map {\operatorname {conv} } U$ by:

$\ds \map {\operatorname {conv} } U = \set {\sum_{j \mathop = 1}^n \lambda_j u_j : n \in \N, \, u_j \in U \text { and } \lambda_j \in \R_{> 0} \text { for each } j, \, \sum_{j \mathop = 1}^n \lambda_j = 1}$

Also see

  • Results about convex hulls can be found here.