  Hyperbolicity cones are convex algebraic cones arising from hyperbolic
polynomials. A well-understood subclass of hyperbolicity cones is that of
spectrahedral cones and it is conjectured that every hyperbolicity cone is
spectrahedral. In this paper we prove a weaker version of this conjecture by
showing that every smooth hyperbolicity cone is the linear projection of a
spectrahedral cone, that is, a spectrahedral shadow.
