Conical combination

The name derives from the fact that the set of all conical sum of vectors defines a cone (possibly in a lower-dimensional subspace).

[2] That is, By taking k = 0, it follows the zero vector (origin) belongs to all conical hulls (since the summation becomes an empty sum).

In fact, it is the intersection of all convex cones containing S plus the origin.

[1] Moreover, the above remark about dividing the coefficients while discarding the origin implies that the conical combinations and hulls may be considered as convex combinations and convex hulls in the projective space.

Moreover, it is not even necessarily a closed set: a counterexample is a sphere passing through the origin, with the conical hull being an open half-space plus the origin.

In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin plus the origin.