A convex combination of vectors 
in a real vector
space is a linear combination
 |
whose coefficients satisfy 
and 
. A subset 
of a vector
space is convex if it contains every convex combination
of finitely many of its points. Equivalently, 
is convex if 
for all 
and 
.
The set of all convex combinations of points in 
is the convex hull of 
. In particular, the convex combinations
of two distinct points 
and 
form the line segment joining
them.
