group trace

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number of important properties about the structures of groups, many of which are most easily expressed in terms of characters. In essence, group characters can be thought of as the matrix traces of a special set of matrices (a so-called irreducible representation) used to represent group elements and whose multiplication corresponds to the multiplication table of the group.

character table | conjugacy class | finite group | group | group orthogonality theorem | matrix trace