positive root

If $R\subset E$ is a root system, with $E$ an Euclidean vector space, then a subset $R^{+}\subset R$ is called a set of positive roots if there is a vector $v\in E$ such that $(\alpha ,v)>0$ if $\alpha \in R^{+}$, and if $\alpha \in R\backslash R^{+}$. http://planetmath.org/node/3645Roots which are not positive are called negative. Since $-\alpha$ is negative if and only if $\alpha$ is positive, exactly half the must be positive.

Title	positive root
Canonical name	PositiveRoot
Date of creation	2013-03-22 13:11:46
Last modified on	2013-03-22 13:11:46
Owner	mathwizard (128)
Last modified by	mathwizard (128)
Numerical id	8
Author	mathwizard (128)
Entry type	Definition
Classification	msc 17B20
Defines	negative root