Classical Invariant Theory
Classical Invariant Theory
There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. It also includes a variety of innovations that make this text of interest even to veterans of the subject. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.
- Minimal prerequisites - particularly in algebra
- Applied orientation and practical methods
- Innovative treatments and new results
- Many illustrative examples and exercises
- Extensive references and historical details
Reviews & endorsements
"This is a book that you can start reading knowing nothing whatsoever about the subject and that will get you to the point where you can start your own research. In fact, when you read it, you may want to start working immediately." -Mathematical Reviews
"As a modern in-depth study of binary forms, this book is one of a kind." -Bulletin of the American Mathematical Society
Product details
January 1999Hardback
9780521552431
304 pages
237 × 161 × 24 mm
0.57kg
7 b/w illus. 10 tables 122 exercises
Available
Table of Contents
- Introduction
- Notes to the reader
- A brief history
- Acknowledgements
- 1. Prelude - quadratic polynomials and quadratic forms
- 2. Basic invariant theory for binary forms
- 3. Groups and transformations
- 4. Representations and invariants
- 5. Transvectants
- 6. Symbolic methods
- 7. Graphical methods
- 8. Lie groups and moving frames
- 9. Infinitesimal methods
- 10. Multi-variate polynomials
- References
- Author index
- Subject index.
