Definition:Convex Cone

Definition

Let $\GF \in \set {\R, \C}$.

Let $X$ be a vector space over $\GF$.

Let $P \subseteq X$ be a cone in $X$.

We say that $P$ is a convex cone if and only if:

for each $v, v' \in P$, we have $v + v' \in P$.

Also see

• Convex Cone is Convex Set

Sources

• 2023: Jean-Bernard Bru and Walter Alberto de Siqueira Pedra: C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics ... (previous) ... (next): $1.1$: Basic notions