Definition
Affine Combination
Let
, where is a vector space over the scalar field , and let satisfy Then the sum
is called an affine combination of
. The condition
distinguishes affine combinations from general linear combinations.
Trivial
Trivial Affine Combination
An affine combination is called trivial if exactly one coefficient is
and all others are , i.e. for some , In this case, the affine combination is just
.