The theory of symmetric positive operators provides a setting to study a large class of partial differentlal equations in a unified way. First introduced by Friedrichs in 1958, they now serve as the theoretical foundation of various DG methods and have recently also received attention from the model order reduction community. In this talk we will give a basic introduction to the theory and discuss implications for the approximability of parametrized PDEs. We show our recent results for the linear advection-reaction equation and discuss future applications.