convex combination
Let be some vector space over . Let be some set of elements of . Then a convex combination of elements from is a linear combination of the form
for some , where each , each and .
Let be the set of all convex combinations from . We call the convex hull, or convex envelope, or convex closure of . It is a convex set, and is the smallest convex set which contains . A set is convex if and only if .
Title | convex combination |
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Canonical name | ConvexCombination |
Date of creation | 2013-03-22 11:50:36 |
Last modified on | 2013-03-22 11:50:36 |
Owner | mps (409) |
Last modified by | mps (409) |
Numerical id | 14 |
Author | mps (409) |
Entry type | Definition |
Classification | msc 52A01 |
Synonym | convex hull |
Synonym | convex envelope |
Synonym | convex closure |
Related topic | ConvexSet |
Related topic | AffineCombination |