Convex hull

Stub grade: C

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

Not really important, references would be good

Definition

Let $S\in\mathcal{P}(\mathbb{R}^n)$ be an an arbitrary subset of $\mathbb{R}^n$ - that is not empty - we define the convex hull, $H$ as follows:

• $$H:\eq\bigcap_{C\in\text{Convex}(S;\mathbb{R}^n)}C$$ - the intersection of all convex sets in $\mathbb{R}^n$ containing $S$
  • Here $\text{Convex}(A;\mathbb{R}^p)$ denotes all the convex sets in $\mathbb{R}^p$ that contain $A$

See also

• Standard $n$-simplex - the convex hull of $(n+1)$-geometrically independent points