A [spectrahedron][1] is a convex set defined by a linear matrix inequality (LMI). 

Is the boundary of such a set almost always smooth? 

By "smooth" I mean that it admits a tangent hyperplane at any point of the surface. I say "almost" because, for the special case of the polytope, the boundary has many "edges". In this special case, the answer would be no.


  [1]: https://en.wikipedia.org/wiki/Spectrahedron