Convex Cone

Last updated Nov 1, 2022

Let $V$ be a Vector Space over $\mathbb{R}$ and let $S \subset V$. Then $S$ is a Convex Cone if $\forall a, b \geq 0$ we have that $$a \mathbf{u} + b \mathbf{v} \in S$$ $\forall \mathbf{u}, \mathbf{v} \in S$.

1. A Convex Cone is a Convex Set - this justifies the name.