  Spectrahedra are linear sections of the cone of positive semidefinite
matrices that, as convex bodies, generalize the class of polyhedra. In this
paper we investigate the problem of recognizing when a spectrahedron is
polyhedral. We reprove a result of Ramana (1998) regarding the structure of
spectrahedra and we devise a normal form of representations of spectrahedra.
This normal form is effectively computable and leads to an algorithm for
deciding polyhedrality.
