Cone

Dependencies:

1. Vector Space

Let $V$ be a vector space over $\mathbb{R}$. Let $S \subseteq V$. Then $S$ is a cone iff \[ \forall x \in S, \forall \alpha \ge 0, \alpha x \in S. \] $S$ is said to be pointed if $\forall x \in S - \{0\}, -x \not\in S$.

Dependency for:

1. Direction of a convex set and Recession cone
2. Extreme direction of convex cone as extreme point of intersection with hyperplane
3. Recession cone of a polyhedron
4. Polyhedral set and polyhedral cone

Info:

• Depth: 4
• Number of transitive dependencies: 4

Transitive dependencies:

1. Group
2. Ring
3. Field
4. Vector Space