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Exterior Algebras

Exterior Algebras
Elementary Tribute to Grassmann's Ideas

by Vincent Pavan

  • Publisher : Elsevier
  • Release : 2017-05-25
  • Pages : 208
  • ISBN : 0081023480
  • Language : En, Es, Fr & De
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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

Tensor Spaces and Exterior Algebra

Tensor Spaces and Exterior Algebra
A Book

by Takeo Yokonuma

  • Publisher : American Mathematical Soc.
  • Release : 1992
  • Pages : 131
  • ISBN : 9780821827963
  • Language : En, Es, Fr & De
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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 applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Lectures on Exterior Algebras Over Commutative Rings

Lectures on Exterior Algebras Over Commutative Rings
A Book

by Robert B. Gardner

  • Publisher : Unknown Publisher
  • Release : 1972
  • Pages : 224
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Linear Algebra via Exterior Products

Linear Algebra via Exterior Products
A Book

by Sergei Winitzki

  • Publisher : Sergei Winitzki
  • Release : 2010-01-04
  • Pages : 285
  • ISBN : 140929496X
  • Language : En, Es, Fr & De
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This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.

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
A Book

by Johan G. F. Belinfante,Bernard Kolman

  • Publisher : SIAM
  • Release : 1989-01-01
  • Pages : 164
  • ISBN : 9781611971330
  • Language : En, Es, Fr & De
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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 itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Algebra I

Algebra I
Chapters 1-3

by N. Bourbaki

  • Publisher : Springer Science & Business Media
  • Release : 1998-08-03
  • Pages : 710
  • ISBN : 9783540642435
  • Language : En, Es, Fr & De
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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.

Tensor Spaces and Exterior Algebra

Tensor Spaces and Exterior Algebra
A Book

by Takeo Yokonuma

  • Publisher : Springer Science & Business
  • Release : 1992
  • Pages : 131
  • ISBN : 9780821845646
  • Language : En, Es, Fr & De
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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. 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 applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

The Algebraic Theory of Spinors and Clifford Algebras

The Algebraic Theory of Spinors and Clifford Algebras
Collected Works

by Claude Chevalley

  • Publisher : Springer Science & Business Media
  • Release : 1996-12-13
  • Pages : 214
  • ISBN : 9783540570639
  • Language : En, Es, Fr & De
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In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.

Linear Algebra and Geometry

Linear Algebra and Geometry
A Book

by Igor R. Shafarevich,Alexey O. Remizov

  • Publisher : Springer Science & Business Media
  • Release : 2012-08-23
  • Pages : 526
  • ISBN : 3642309941
  • Language : En, Es, Fr & De
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This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Quadratic Mappings and Clifford Algebras

Quadratic Mappings and Clifford Algebras
A Book

by Jacques Helmstetter,Artibano Micali

  • Publisher : Springer Science & Business Media
  • Release : 2008-05-24
  • Pages : 504
  • ISBN : 9783764386061
  • Language : En, Es, Fr & De
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After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.

Multilinear Algebra

Multilinear Algebra
A Book

by Werner H. Greub

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 224
  • ISBN : 3662007959
  • Language : En, Es, Fr & De
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This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but exc1uded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. These results are extended in Chapter 11 to vector spaces with additional structure, such as algebras and differ ential spaces. The fundamental concept of "tensor product" is used in Chapter 111 to construct the tensor algebra over a given vector space. In the next chapter the link is provided between tensor algebra on the one hand and exterior and symmetrie tensor algebra on the other. Chapter V contains material on exterior algebra which is developed in considerable depth. Exterior algebra techniques are used in the followmg chapter as a powerful tool to obtain matrix-free proofs of many classical theorems on linear transformation.

Advanced Linear Algebra

Advanced Linear Algebra
A Book

by Bruce Cooperstein

  • Publisher : CRC Press
  • Release : 2016-04-19
  • Pages : 364
  • ISBN : 1439829691
  • Language : En, Es, Fr & De
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Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material. Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra. It also prepares them for further study in mathematics.

Triple Multiplicities for Sl(R+1) and Spectrum of the Exterior Algebra of Adjoint Representation

Triple Multiplicities for Sl(R+1) and Spectrum of the Exterior Algebra of Adjoint Representation
A Book

by A. D. Berenstein,A. V. Zelevinsky

  • Publisher : Unknown Publisher
  • Release : 1990
  • Pages : 42
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Algebra Colloquium

Algebra Colloquium
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Linear Algebra

Linear Algebra
A Book

by Harold M. Edwards

  • Publisher : Springer Science & Business Media
  • Release : 2004-10-15
  • Pages : 184
  • ISBN : 9780817643706
  • Language : En, Es, Fr & De
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* Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject

Russian Mathematics

Russian Mathematics

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1999
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Siberian Mathematical Journal

Siberian Mathematical Journal
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1968
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Stably Flat Completions of Universal Enveloping Algebras

Stably Flat Completions of Universal Enveloping Algebras
A Book

by A. Yu Pirkovskii

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 60
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Exterior Calculus

Exterior Calculus
A Book

by Howard Osborn

  • Publisher : Unknown Publisher
  • Release : 1969
  • Pages : 221
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Basic Algebra

Basic Algebra
A Book

by Anthony W. Knapp

  • Publisher : Springer Science & Business Media
  • Release : 2006-09-28
  • Pages : 717
  • ISBN : 0817632484
  • Language : En, Es, Fr & De
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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.