  An elimination problem in semidefinite programming is solved by means of
tensor algebra. It concerns families of matrix cube problems whose constraints
are the minimum and maximum eigenvalue function on an affine space of symmetric
matrices. An LMI representation is given for the convex set of all feasible
instances, and its boundary is studied from the perspective of algebraic
geometry. This generalizes the earlier work [12] with Parrilo on k-ellipses and
k-ellipsoids.
