The Polynomial Identities And Invariants Of N Times N Matrices
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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.
The Polynomial Identities And Invariants Of N X N Matrices
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Author : Edward Formanek
language : en
Publisher: American Mathematical Soc.
Release Date :
The Polynomial Identities And Invariants Of N X 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 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.
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 Mathematics 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.
Computational Aspects Of Polynomial Identities
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Author : Alexei Kanel-Belov
language : en
Publisher: CRC Press
Release Date : 2015-10-22
Computational Aspects Of Polynomial Identities written by Alexei Kanel-Belov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
Computational Aspects of Polynomial Identities: Volume l, Kemer's Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0.The
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Author : Eli Aljadeff
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-14
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras written by Eli Aljadeff 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 2020-12-14 with Education categories.
A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Well Posedness Of The Cauchy Problem For N Times N Systems Of Conservation Laws
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Author : Alberto Bressan
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Well Posedness Of The Cauchy Problem For N Times N Systems Of Conservation Laws written by Alberto Bressan 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 2000 with Mathematics categories.
This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras
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Author : Eliahu Aljadeff
language : en
Publisher: American Mathematical Soc.
Release Date : 2020
Rings With Polynomial Identities And Finite Dimensional Representations Of Algebras written by Eliahu Aljadeff 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 2020 with Education categories.
Noncommutative algebra -- Universal algebra -- Symmetric functions and matrix invariants -- Polynomial maps -- Azumaya algebras and irreducible representations -- Tensor symmetry -- Growth -- Shirshov's theorem -- 2 x 2 matrices -- Matrix identities -- Structure theorems -- Invariants and trace identities -- Involutions and matrices -- A geometric approach -- Spectrum and dimension -- The nilpotent radical -- Finite dimensional and affine PI algebras -- The relatively free algebras -- Identities and superalgebras -- The Specht problem -- The PI-exponent -- Codimension growth for matrices -- Codimension growth for algebras satisfying a Capelli identity.
Invitation To Nonlinear Algebra
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Author : Mateusz Michałek
language : en
Publisher: American Mathematical Society
Release Date : 2021-03-05
Invitation To Nonlinear Algebra written by Mateusz Michałek and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-05 with Mathematics categories.
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
Collected Papers Of R S Rivlin
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Author : Grigory I. Barenblatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Collected Papers Of R S Rivlin written by Grigory I. Barenblatt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Technology & Engineering categories.
R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1971
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Nuclear energy categories.