the notion of convexity of vector spaces can be generalized to dimension-free sets of matrices. a natural question that then arises is how to identify a set's matrix convex hull. we introduce some techniques for getting a grasp on the matrix convex hull of semi-algebraic sets and look at one of these in particular: the bent tv screen. this is the set $$ \{ (x, y) : i - x^2 - y^4 \succeq 0 \} $$ it is convex in the scalar case but is not matrix convex. in fact, there is no known "simple" formula for its matrix convex hull.