Mathematical Preliminaries

Abstract

For the reader’s convenience we shall quickly review linear algebra and the rudiments of linear dynamic systems. In keeping with the spirit of this book we emphasize the geometric content of the mathematical foundations, laying stress on the presentation of results in terms of vector spaces and their subspaces. As the material is standard, few proofs are offered; however, detailed developments can be found in the textbooks cited at the end of the chapter. For many of the simpler identities involving maps and subspaces, the reader is invited to supply his own proofs; an illustration and further hints are provided in the exercises. It is also recommended that the reader gain practice in translating geometric statements into matrix formalism, and vice versa; for this, guidance will also be found in the exercises.