Definition: Convex Hull

Let \(\mathcal A=(A,V_A,v)\) be the \(n\)-dimensional affine space with \(V_A\) as the associated vector space over the field \(\mathbb R\) of real numbers. Let \(X\subseteq\mathcal A\) be a subset. The convex hull of \(X\) can be constructed as the intersection of all convex sets \(Y\) that contain \(X\):

\[\operatorname{conv}(X):=\bigcap\{Y\subseteq \mathcal A\,:\,X\subseteq Y\,,\,Y\text{ convex}\}.\]


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References

Bibliography

  1. Ziegler, G√ľnter M.: "Lectures on Polytopes", Springer Verlag, 1994