Coordinated linear systems are a particular class of hierarchical systems with a top-to-bottom information structure, consisting of a coordinator system and two or more subsystems. This paper deals with the construction and minimality of coordinated linear systems. Construction procedures are given to transform unstructured or interconnected systems into coordinated linear systems, using the geometric (i.e. basis-independent) concepts of observability and controllability subspaces. Several concepts of minimality for coordinated linear systems are suggested and characterized in order to identify decompositions which are 'as decentralized as possible'. The extension of the developed methods and results to the broader class of hierarchical linear systems is discussed. © 2014 Elsevier Inc.