Let L be a linear transformation on a finite dimensional real Hilbert space H and K be a closed convex cone with dual K* in H. The cone spectrum of L relative to K is the set of all real \lambda for which the linear complementarity problem $x in K, y=L(x)-\lambda x in K*, and x perpendicular to y$ admits a nonzero solution x. In the setting of a Euclidean Jordan algebra H and the corresponding symmetric cone K, we discuss the finiteness of the cone spectrum for Z-transformations and quadratic representations on H.
(October 8, 2007)