The Invariant Theory of Matrices

Corrado De Concini, Claudio Procesi

ISBN 10: 147044187X / ISBN 13: 9781470441876

Published by American Mathematical Society, US, 2017

About this Item

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 $m\times m$ 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 the first fundamental theorem that describes a set of generators in the ring of invariants, and 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.

Seller Inventory # LU-9781470441876

Bibliographic Details

• Title: The Invariant Theory of Matrices
• Publisher: American Mathematical Society, US
• Publication Date: 2017
• Language: English
• ISBN 10: 147044187X
• ISBN 13: 9781470441876
• Binding: Paperback
• Condition: New
• Weight: 295 grams

About this title

Synopsis

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 $m\times m$ 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 the first fundamental theorem that describes a set of generators in the ring of invariants, and 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.

About the Author

Corrado De Concini, Sapienza Universita di Roma, Rome, Italy.

Claudio Procesi, Sapienza Universita di Roma, Rome, Italy.