  The image of the cone of positive semidefinite matrices under a linear map is
a convex cone. Pataki characterized the set of linear maps for which that image
is not closed. The Zariski closure of this set is a hypersurface in the
Grassmannian. Its components are the coisotropic hypersurfaces of symmetric
determinantal varieties. We develop the convex algebraic geometry of such bad
projections, with focus on explicit computations.
