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Exterior Algebras

Exterior Algebras
  • Author : Vincent Pavan
  • Publsiher : Elsevier
  • Release : 25 May 2017
  • ISBN : 0081023480
  • Pages : 208 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKExterior Algebras

Summary:
Exterior Algebras: Elementary Tribute to Grassmann's Ideas provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann's algebras. Then, it shows how the latter can be used to treat a few basic, though significant, questions of linear algebra, such as co-linearity, determinant calculus, linear systems analyzing, volumes computations, invariant endomorphism considerations, skew-symmetric operator studies and decompositions, and Hodge conjugation, amongst others. Presents a self-contained guide that does not require any specific algebraic background Includes numerous examples and direct applications that are suited for beginners


Exterior Algebras

Exterior Algebras
  • Author : Vincent Pavan
  • Publisher : Elsevier
  • Release : 25 May 2017
GET THIS BOOKExterior Algebras

Exterior Algebras: Elementary Tribute to Grassmann's Ideas provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann's algebras. Then, it shows how the latter can be used to treat a few basic, though significant, questions of linear algebra, such as co-linearity, determinant calculus, linear systems analyzing, volumes computations, invariant endomorphism considerations, skew-symmetric operator studies and decompositions, and Hodge conjugation, amongst others. Presents a self-contained guide that does not require any specific algebraic

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Tensor Spaces and Exterior Algebra

Tensor Spaces and Exterior Algebra
  • Author : Takeo Yokonuma
  • Publisher : American Mathematical Soc.
  • Release : 23 May 1992
GET THIS BOOKTensor Spaces and Exterior Algebra

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and

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From Vectors to Tensors

From Vectors to Tensors
  • Author : Juan R. Ruiz-Tolosa,Enrique Castillo
  • Publisher : Springer Science & Business Media
  • Release : 30 March 2006
GET THIS BOOKFrom Vectors to Tensors

This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

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A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods
  • Author : Johan G. F. Belinfante,Bernard Kolman
  • Publisher : SIAM
  • Release : 01 January 1989
GET THIS BOOKA Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory

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Algebra I

Algebra I
  • Author : N. Bourbaki
  • Publisher : Springer Science & Business Media
  • Release : 03 August 1998
GET THIS BOOKAlgebra I

An exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, and the third investigatesalgebras, particularly tensor algebras.

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Handbook of Mathematics

Handbook of Mathematics
  • Author : Vialar Thierry
  • Publisher : BoD - Books on Demand
  • Release : 04 April 2017
GET THIS BOOKHandbook of Mathematics

The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts

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Clifford Algebras and Lie Theory

Clifford Algebras and Lie Theory
  • Author : Eckhard Meinrenken
  • Publisher : Springer Science & Business Media
  • Release : 28 February 2013
GET THIS BOOKClifford Algebras and Lie Theory

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–

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Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups
  • Author : Alexander J. Hahn
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKQuadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras,

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Lie Groups

Lie Groups
  • Author : Claudio Procesi
  • Publisher : Springer Science & Business Media
  • Release : 17 October 2007
GET THIS BOOKLie Groups

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. In Lie Groups: An Approach through Invariants and Representations, the author's masterful approach gives the reader a comprehensive treatment of the classical Lie groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory,

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Supersymmetry for Mathematicians: An Introduction

Supersymmetry for Mathematicians: An Introduction
  • Author : V. S. Varadarajan
  • Publisher : American Mathematical Soc.
  • Release : 23 May 2022
GET THIS BOOKSupersymmetry for Mathematicians: An Introduction

Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles

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Modules and Rings

Modules and Rings
  • Author : John Dauns
  • Publisher : Cambridge University Press
  • Release : 28 October 1994
GET THIS BOOKModules and Rings

This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products.

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