Trivial Convex Combination

linear-algebra convex-geometry

Definition

Trivial Convex Combination

A convex combination ${\sum }_i{\lambda }_i{\mathbf{v}}_i$ is trivial if exactly one coefficient is $1$ and all others are $0$. In this case, the combination equals ${\mathbf{v}}_k$ for the index $k$ with ${\lambda }_k=1$.