Abstract: The aim of this note is to compute the Grothendieck group of the category of endomorphisms. This computation mostly plays with linear algebra. The main result is that in , every endomorphism is uniquely characterized by and its characteristic polynomial . This computation was due to . We will explain how to think about this computation, the reason for certain constructions and the “diagonalization” in this computation.
 Almkvist, G. (1974). The Grothendieck ring of the category of endomorphisms. Journal of Algebra, 28(3), 375-388.