The Invariant Theory of Matrices

The Invariant Theory of Matrices
Author :
Publisher : American Mathematical Soc.
Total Pages : 162
Release :
ISBN-10 : 9781470441876
ISBN-13 : 147044187X
Rating : 4/5 (87X Downloads)

Book Synopsis The Invariant Theory of Matrices by : Corrado De Concini

Download or read book The Invariant Theory of Matrices written by Corrado De Concini and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.


The Invariant Theory of Matrices Related Books

The Invariant Theory of Matrices
Language: en
Pages: 162
Authors: Corrado De Concini
Categories: Mathematics
Type: BOOK - Published: 2017-11-16 - Publisher: American Mathematical Soc.

GET EBOOK

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free appr
Invariant Subspaces of Matrices with Applications
Language: en
Pages: 706
Authors: Israel Gohberg
Categories: Mathematics
Type: BOOK - Published: 2006-03-01 - Publisher: SIAM

GET EBOOK

This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebra
Matrix Theory
Language: en
Pages: 290
Authors: Fuzhen Zhang
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

GET EBOOK

This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techn
Random Matrix Theory
Language: en
Pages: 236
Authors: Percy Deift
Categories: Mathematics
Type: BOOK - Published: 2009-01-01 - Publisher: American Mathematical Soc.

GET EBOOK

"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and s
Lectures on Invariant Theory
Language: en
Pages: 244
Authors: Igor Dolgachev
Categories: Mathematics
Type: BOOK - Published: 2003-08-07 - Publisher: Cambridge University Press

GET EBOOK

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal back