A framework is a finite configuration of points in a Euclidean space, where some pairs of the points are connected by fixed length bars. Such a framework is universally rigid if any other configuration in any dimensional Euclidean space with the same bar lengths is congruent to it. We prove a complete characterization of when a framework is universally rigid that relies on a sequence of stress matrices. These ideas are inspired by a theory of facial reduction in convexity theory, and it is closely related to the theory of tensegrity structures, where each bar constraint is weakened to have an upper or lower bound on the length of each edge of the underlying graph. This is joint work with Shlomo Gortler.