Elements of System Theory
This chapter is devoted to a short introduction to algebraic system theory. We shall focus on the main conceptual underpinnings of the theory, more specifically on the themes of external and internal representations of systems and the associated realization theory. We feel that these topics are to be considered as an essential part of linear algebra. In fact, the notions of reachability and observability, introduced by Kaiman (see Kaiman  and the references within), fill a gap that the notion of cyclicity leaves open. Also, they have such a strong intuitive appeal that it will be rather perverse not to use them and search instead for sterile, but “pure” substitute terms.
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