Cones

Let .

A conic combination of is a linear combination where .

The conic hull of is the set of conic combinations, are conically dependent whenever for some not all zero. Otherwise, are conically independent.

Let for some , and let . Then if and only if there exists a such that and for every .

In other words, if and only if and are on opposite sides of some hyperplane .

Let for some . Then are conically independent if and only if there exists a such that for every nonzero .

In other words, are conically independent if and only if is strictly on one side of some hyperplane .