Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 42–43 页 · Section 9.1「Reflections in a euclidean space」中的空间、反射约定及 Section 9.2「Root systems」中的定义（省略中间的证明与说明）
Throughout this chapter we are concerned with a fixed euclidean space $E$, i.e., a finite dimensional vector space over $\mathbb R$ endowed with a positive definite symmetric bilinear form $(\alpha,\beta)$. […] Any nonzero vector $\alpha$ determines a reflection $\sigma_\alpha$, with reflecting hyperplane $P_\alpha=\{\beta\in E\mid(\beta,\alpha)=0\}$. […] Let $\Phi$ be a root system in $E$. Denote by $\mathcal W$ the subgroup of $GL(E)$ generated by the reflections $\sigma_\alpha$ $(\alpha\in\Phi)$. […] $\mathcal W$ is called the Weyl group of $\Phi$, and plays an extremely important role in the sequel.