Example 2

Consider the specific case when A is the algebra End$_K(V)$ of endomorphisms of a finite-dimensional K-vector space V. Taking M to be the simple A-module V, we obtain the relations

Pcrd$_{A/K}(u; X) =\chi_u(X)$,

(27) Nrd$_{A/K}(u) =$ det($u$),

Trd$_{A/K}(u) =$ Tr($u$)

for every endomorphism $u$ of V.