# simple root

Let $R\subseteq E$ be a root system, with $E$ a Euclidean vector space (http://planetmath.org/VectorSpace). 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.