ScalingStacks

Definition 3.67 . [02MH]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Definition 3.67.

The dual of a convex cone σ⊂Nℝ\sigma\subset N_{\mathbb{R}} is defined as

σ∨={x∈Mℝ∣⟨x,u⟩≥0​ for all ​u∈σ}.\sigma^{\vee}=\{x\in M_{\mathbb{R}}\mid\langle x,u\rangle\geq 0\text{ for all }u\in\sigma\}.

This is a convex closed cone.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.