伦敦数学会学生系列：皮特·奥立弗：经典不变理论 Classical Invariant Theory

基本信息

Format Paperback | 304 pages

Dimensions 153 x 229 x 19mm | 405g

Publication date 15 Feb 2003

Publisher Cambridge University Press

ISBN10 0521558212

ISBN13 9780521558211

仅供参考，具体以实物为主

书籍简介

在以下几个因素的推动下，人们对经典不变量理论的兴趣再度升温：新的理论发展；计算方法的复兴，加上强大的新计算机代数软件包；以及大量的新应用，从数论到几何，从物理到计算机视觉。本书为读者提供了关于经典理论以及现代发展和应用的单独介绍。

文本集中于研究特征零中的二元形式（多项式），并使用分析以及代数工具来研究和分类不变量、对称性、等价性和典型形式。它还包括各种创新，使这个文本甚至对这个主题的老手都感兴趣。本书针对高年级本科生和研究生，包括许多练习和历史细节，基本定理的完整证明，以及生动和挑衅性的阐述。

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.

作者简介

By (author) Peter J. Olver

皮特·奥立弗（1952年1月11日，特威克纳姆）是一位从事微分几何研究的英美数学家。

Peter John Olver (11 January 1952, Twickenham) is a British-American mathematician working in differential geometry.

目录

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.