A subset 
of a vector space 
is said to be convex if 
for all vectors 
, and all scalars ![lambda in [0,1]](/images/equations/ConvexCombination/Inline5.svg)
. Via induction, this can be seen to be equivalent
to the requirement that 
for all vectors 
, and for all scalars 
such that 
. With the above restrictions on the 
, an expression of the form 
is said to be a convex combination
of the vectors 
.
The set of all convex combinations of vectors in 
constitute the convex hull
of 
so, for example, if 
are two different vectors in the vector space 
, then the set of all convex combinations
of 
and 
constitute the line segment between 
and 
.
