The Relation between the Mandelstam and the Cayley-Hamilton Identities

Abstract

Starting from the characteristic polynomial for ordinary matrices we give a combinatorial deduction of the Mandelstam identities and viceversa, thus showing that the two sets of relations are equivalent. We are able to extend this construction to supermatrices in such a way that we obtain the Mandelstam identities in this case, once the corresponding characteristic equation is known.