Let $V$ be a finite-dimensional real [inner product space](/page/Inner%20Product%20Space), and let $\Phi \subset V$ be an irreducible reduced finite root system. Then $\Phi$ is isomorphic to exactly one root system in the following list:
Here isomorphism means a linear isomorphism between the ambient real vector spaces carrying one root system bijectively onto the other and preserving the corresponding Cartan integers.