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Convex hull
From Mathematics Is A Science
Revision as of 16:31, 12 February 2010 by imported>WikiSysop
The idea of convex hull of a set A is the "smallest" convex set that contains A.
The convex hull of two points is the segment that connects them. To capture this set one need some linear algebra.
While the span of vectors in a vector space is defined as the set of all their linear combinations
a0v0 + a1v1 + ... + anvn, a0, ... an are arbitrary real numbers,
the convex hull is defined as the set of all their convex combinations
a0v0 + a1v1 + ... + anvn, a0, ... an are arbitrary real numbers satisfying a0 + ... + an = 1.
For example, a geometric n-simplex is defined as the convex hull of n+1 points in general position:
conv{v0, v1, ..., vn}.