 If "C" is a convex cone, then for any positive scalar "α" and any "x" in "C" the vector formula_1 It follows that a convex cone "C" is a special case of a linear cone.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations, or just under additions.More succinctly, a set "C" is a convex cone if and only if and , for any positive scalar "α".