Consider a collection of diagonal matrices H_1, ..., H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, and is called a weight. The general setting for weights occurs in a Lie algebra representation of a semisimple Lie algebra, in which case the Cartan subalgebra h is Abelian and can be put into diagonal form. For example, consider the standard representation of the special linear Lie algebra s l_3(C) on C^3.

Cartan matrix | Lie algebra | Lie algebra root | root system | semisimple Lie algebra | Weyl group