Une suite de matrices sym\'etriques en rapport avec la fonction de Mertens

In this paper we explore a class of equivalence relations over ${\mathbb{N}}^{\ast }$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of the quadratic norm of these matrices, which implies the Riemann hypothesis. This suggests that matrix analysis methods may play a more important part in this classical and difficult problem.