# Convex hull

From Maths

**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

## Contents

## Definition

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

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

## See also

- Standard [ilmath]n[/ilmath]-simplex - the convex hull of [ilmath](n+1)[/ilmath]-geometrically independent points