  We show that the ring of multisymmetric functions over a commutative ring is
isomorphic to the ring generated by the coefficients of the characteristic
polynomial of polynomials in commuting generic matrices. As a consequence we
give a surjection from the ring of invariants of several matrices to the ring
of multisymmetric functions generalizing a classical result of H.Weyl and
F.Junker. We also find a surjection from the ring of invariants over the
commuting scheme to the ring of multisymmetric functions. This surjection is an
isomophism over a characteristic zero field and induces an isomorphism at the
level of reduced structures over an infinite field of positive characteristic.
