"An introduction to the ideas of algebraic geometry in the motivated
context of system theory." Thus the author describes his textbook that
has been specifically written to serve the needs of students of systems
and control. Without sacrificing mathematical care, the author makes the
basic ideas of algebraic geometry accessible to engineers and applied
scientists. The emphasis is on constructive methods and clarity rather
than abstraction.
The student will find here a clear presentation with an applied flavor,
of the core ideas in the algebra-geometric treatment of scalar linear
system theory. The author introduces the four representations of a
scalar linear system and establishes the major results of a similar
theory for multivariable systems appearing in a succeeding volume (Part
II: Multivariable Linear Systems and Projective Algebraic Geometry).
Prerequisites are the basics of linear algebra, some simple notions from
topology and the elementary properties of groups, rings, and fields, and
a basic course in linear systems. Exercises are an integral part of the
treatment and are used where relevant in the main body of the text. The
present, softcover reprint is designed to make this classic textbook
available to a wider audience.
"This book is a concise development of affine algebraic geometry
together with very explicit links to the applications...[and] should
address a wide community of readers, among pure and applied
mathematicians." --Monatshefte für Mathematik