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Classical Invariant Theory

$62.99 (P)

Part of London Mathematical Society Student Texts

Author: Peter J. Olver, University of Minnesota

Date Published: January 1999
availability: Available
format: Paperback
isbn: 9780521558211

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About the Authors

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. A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. 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
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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
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Product details
- Date Published: January 1999
- format: Paperback
- isbn: 9780521558211
- length: 304 pages
- dimensions: 229 x 153 x 19 mm
- weight: 0.405kg
- contains: 7 b/w illus. 10 tables 122 exercises
- availability: 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.
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