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