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Bilinear Algebra

Author: Kazimierz Szymiczek

Publisher: Routledge

Published: 2017-11-22

Total Pages: 413

ISBN-13: 1351464205

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Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.

Book Synopsis Bilinear Algebra by : Kazimierz Szymiczek

Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.

Bilinear Algebra

Author: Kazimierz Szymiczek

Publisher: Routledge

Published: 2017-11-22

Total Pages: 496

ISBN-13: 1351464213

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Book Synopsis Bilinear Algebra by : Kazimierz Szymiczek

Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.

Bilinear Transformation Method

Author: Matsuno

Publisher: Academic Press

Published: 1984-09-06

Total Pages: 233

ISBN-13: 0080958648

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Bilinear Transformation Method

Book Synopsis Bilinear Transformation Method by : Matsuno

Download or read book Bilinear Transformation Method written by Matsuno and published by Academic Press. This book was released on 1984-09-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bilinear Transformation Method

Neutrosophic Bilinear Algebras and their Generalizations

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

Published: 2010

Total Pages: 404

ISBN-13: 9185917141

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This book introduces over one hundred new concepts related to neutrosophic bilinear algebras and their generalizations. Illustrated by more than 225 examples, these innovative new notions find applications in various fields.

Book Synopsis Neutrosophic Bilinear Algebras and their Generalizations by : W. B. Vasantha Kandasamy

Download or read book Neutrosophic Bilinear Algebras and their Generalizations written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2010 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces over one hundred new concepts related to neutrosophic bilinear algebras and their generalizations. Illustrated by more than 225 examples, these innovative new notions find applications in various fields.

Symmetric Bilinear Forms

Author: John Milnor

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 155

ISBN-13: 3642883303

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The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ...

Book Synopsis Symmetric Bilinear Forms by : John Milnor

Download or read book Symmetric Bilinear Forms written by John Milnor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ...

Bilinear Control Systems

Author: David Elliott

Publisher: Springer Science & Business Media

Published: 2009-09-01

Total Pages: 283

ISBN-13: 1402096135

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The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.

Book Synopsis Bilinear Control Systems by : David Elliott

Download or read book Bilinear Control Systems written by David Elliott and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.

Set Linear Algebra and Set Fuzzy Linear Algebra

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

Published: 2008

Total Pages: 346

ISBN-13: 1599730294

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Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras.These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.

Book Synopsis Set Linear Algebra and Set Fuzzy Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Set Linear Algebra and Set Fuzzy Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2008 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras.These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.

Linear Algebra

Author: E. Sernesi

Publisher: Routledge

Published: 2019-01-22

Total Pages: 274

ISBN-13: 1351435280

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This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finis

Book Synopsis Linear Algebra by : E. Sernesi

Download or read book Linear Algebra written by E. Sernesi and published by Routledge. This book was released on 2019-01-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finis

Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Norbert Euler

Publisher: CRC Press

Published: 2021-09-07

Total Pages: 367

ISBN-13: 1000423301

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The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Norbert Euler

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Norbert Euler and published by CRC Press. This book was released on 2021-09-07 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Linear Algebra

Author: Vivek Sahai

Publisher: Alpha Science Int'l Ltd.

Published: 2002

Total Pages: 208

ISBN-13: 9781842650806

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Beginning with the basic concepts of vector spaces such as linear independence, basis and dimension, quotient space, linear transformation and duality with an exposition of the theory of linear operators on a finite dimensional vector space, this book includes the concepts of eigenvalues and eigenvectors, diagonalization, triangulation and Jordan and rational canonical forms. Inner product spaces which cover finite dimensional spectral theory, and an elementary theory of bilinear forms are also discussed.

Book Synopsis Linear Algebra by : Vivek Sahai

Download or read book Linear Algebra written by Vivek Sahai and published by Alpha Science Int'l Ltd.. This book was released on 2002 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the basic concepts of vector spaces such as linear independence, basis and dimension, quotient space, linear transformation and duality with an exposition of the theory of linear operators on a finite dimensional vector space, this book includes the concepts of eigenvalues and eigenvectors, diagonalization, triangulation and Jordan and rational canonical forms. Inner product spaces which cover finite dimensional spectral theory, and an elementary theory of bilinear forms are also discussed.