The Natural Components of a Regular Linear System

ABSTRACT The analysis of a finite‐dimensional regular linear system may be simplified by separating the system into its natural components. The natural components are smaller linear systems on separate subspaces whose dimensions sum to the dimension of the original linear system. Each natural component has a single eigenvalue and may be studied in isolation. By reassembling the natural components we obtain a general characterisation of the set of all solutions to the original linear system which contains the core content of the Granger‐Johansen theorem.