Let $E$ be a finite-dimensional real [inner product space](/page/Inner%20Product%20Space), and let $\Phi \subset E$ be a finite root system. For each root $\alpha \in \Phi$, write
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\begin{align*}
H_\alpha := \{v \in E : (\alpha,v)=0\}.
\end{align*}
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A Weyl chamber is a connected component of
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\begin{align*}
E \setminus \bigcup_{\alpha \in \Phi} H_\alpha.
\end{align*}
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For a Weyl chamber $C$, define
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\begin{align*}
\Phi_C^+ := \{\alpha \in \Phi : (\alpha,v)>0 \text{ for every } v \in C\}.
\end{align*}
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Then the assignment
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\begin{align*}
C \longmapsto \Phi_C^+
\end{align*}
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is a bijection from the set of Weyl chambers of $\Phi$ onto the set of positive systems in $\Phi$.