# 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 |