The Invariant Theory Of Matrices
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The Invariant Theory Of Matrices
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Author : Corrado De Concini
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-16
The Invariant Theory Of Matrices written by Corrado De Concini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Invariants categories.
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 Theory Of Determinants Matrices And Invariants
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Author : Herbert Westren Turnbull
language : en
Publisher:
Release Date : 1948
The Theory Of Determinants Matrices And Invariants written by Herbert Westren Turnbull and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Determinants categories.
The Theory Of Determinants Matrices And Invariants
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Author : Herbert Westren Turnbull
language : en
Publisher:
Release Date : 1960
The Theory Of Determinants Matrices And Invariants written by Herbert Westren Turnbull and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Determinants categories.
Algebraic Homogeneous Spaces And Invariant Theory
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Author : Frank D. Grosshans
language : en
Publisher: Springer
Release Date : 2006-11-14
Algebraic Homogeneous Spaces And Invariant Theory written by Frank D. Grosshans and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.
Invariant Theory Of Finite Groups
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-03-08
Invariant Theory Of Finite Groups written by Mara D. Neusel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-08 with Mathematics categories.
The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.
The Polynomial Identities And Invariants Of N Times N Matrices
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Author : Edward Formanek
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
The Polynomial Identities And Invariants Of N Times N Matrices written by Edward Formanek and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.
Invariant Theory Old And New
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Author : Jean Alexandre Dieudonné
language : en
Publisher:
Release Date : 1971
Invariant Theory Old And New written by Jean Alexandre Dieudonné and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Invariant Theory
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Invariant Theory written by Mara D. Neusel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Invariants categories.
This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.
Invariant Theory
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Author : Sebastian S. Koh
language : en
Publisher: Springer
Release Date : 2006-11-15
Invariant Theory written by Sebastian S. Koh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. This collection of papers centers on constructive aspects of invariant theory and opens with an introduction to the subject by F. Grosshans. Its purpose is to make the current research more accesssible to mathematicians in related fields.
Invariant Subspaces Of Matrices With Applications
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Author : Israel Gohberg
language : en
Publisher: SIAM
Release Date : 2006-03-01
Invariant Subspaces Of Matrices With Applications written by Israel Gohberg and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.
This unique book addresses advanced linear algebra using invariant subspaces as the central notion and main tool. It comprehensively covers geometrical, algebraic, topological, and analytic properties of invariant subspaces, laying clear mathematical foundations for linear systems theory with a thorough treatment of analytic perturbation theory for matrix functions.