A quiver approach to studying orbit spaces of linear systems

Orbit spaces associated to linear actions are of particular interest in control theory. Their geometrical properties can be naturally investigated by using the representations of quivers as an abstract framework. The aim of the paper is to bring into attention an application of this approach and to show how the use of quivers makes it easy handling concepts arising in control theory. Specifically, the natural duality between controllable and observable systems, as well as the construction of compactifications for the associated orbit spaces is interpreted in terms of opposite quivers.