  We continue the investigation on the spectrum of operators arising from the
discretization of partial differential equations. In this paper we consider a
three field formulation recently introduced for the finite element
least-squares approximation of linear elasticity. We discuss in particular the
distribution of the discrete eigenvalues in the complex plane and how they
approximate the positive real eigenvalues of the continuous problem. The
dependence of the spectrum on the Lam\'e parameters is considered as well and
its behavior when approaching the incompressible limit.
