Let $R\subseteq E$ be a root system, with $E$ a Euclidean vector space. If $R^+$ is a set of positive roots, then a root is called simple if it is positive, and not the sum of any two positive roots. The simple roots form a basis of the vector space $E$ , and any positive root is a positive integer linear combination of simple roots.

A set of roots which is simple with respect to some choice of a set of positive roots is called a base. The Weyl group of the root system acts simply transitively on the set of bases.