Definition:Cone (Vector Space)
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Definition
Let $\GF \in \set {\R, \C}$.
Let $X$ be a vector space over $\GF$.
Let $P \subseteq X$.
We say that $P$ is a cone if and only if:
- for all $\alpha \in \R_{\ge 0}$ and $v \in P$, we have $\alpha v \in P$.
Sources
- 2023: Jean-Bernard Bru and Walter Alberto de Siqueira Pedra: C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics ... (next): $1.1$: Basic notions