# generalized Cartan matrix

A generalized Cartan matrix is a matrix $A$ whose diagonal^{} entries are all 2, and whose off-diagonal entries are nonpositive integers, such that ${a}_{ij}=0$ if and only if ${a}_{ji}=0$. Such a matrix is called symmetrizable if there is a diagonal matrix^{} $B$ such that $AB$ is symmetric^{}.

Title | generalized Cartan matrix |
---|---|

Canonical name | GeneralizedCartanMatrix |

Date of creation | 2013-03-22 13:52:56 |

Last modified on | 2013-03-22 13:52:56 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 5 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 17B67 |

Related topic | ExtendedCartanMatrix |

Defines | symmetrizable |