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Exterior Algebras

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Exterior Algebras

Exterior Algebras Book
Author : Vincent Pavan
Publisher : Elsevier
Release : 2017-05-25
ISBN : 0081023480
Language : En, Es, Fr & De

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Book Description :

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

Lectures on Exterior Algebras Over Commutative Rings

Lectures on Exterior Algebras Over Commutative Rings Book
Author : Robert B. Gardner
Publisher : Unknown
Release : 1972
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Lectures on Exterior Algebras Over Commutative Rings book written by Robert B. Gardner, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Tensor Spaces and Exterior Algebra

Tensor Spaces and Exterior Algebra Book
Author : Takeo Yokonuma
Publisher : American Mathematical Soc.
Release : 1992
ISBN : 9780821827963
Language : En, Es, Fr & De

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Book Description :

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.

Tensor Spaces and Exterior Algebra

Tensor Spaces and Exterior Algebra Book
Author : Takeo Yokonuma
Publisher : Springer Science & Business
Release : 1992
ISBN : 9780821845646
Language : En, Es, Fr & De

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Book Description :

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.

Algebra I

Algebra I Book
Author : N. Bourbaki
Publisher : Springer Science & Business Media
Release : 1998-08-03
ISBN : 9783540642435
Language : En, Es, Fr & De

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Book Description :

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.

Exterior Calculus

Exterior Calculus Book
Author : Howard Osborn
Publisher : Unknown
Release : 1969
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Exterior Calculus book written by Howard Osborn, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Linear Algebra via Exterior Products

Linear Algebra via Exterior Products Book
Author : Sergei Winitzki
Publisher : Sergei Winitzki
Release : 2010-01-04
ISBN : 140929496X
Language : En, Es, Fr & De

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Book Description :

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.

Algebra Colloquium

Algebra Colloquium Book
Author : Anonim
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Algebra Colloquium book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Stably Flat Completions of Universal Enveloping Algebras

Stably Flat Completions of Universal Enveloping Algebras Book
Author : A. Yu Pirkovskii
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Stably Flat Completions of Universal Enveloping Algebras book written by A. Yu Pirkovskii, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Multilinear Algebra

Multilinear Algebra Book
Author : Werner H. Greub
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3662007959
Language : En, Es, Fr & De

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Book Description :

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.

Hasse Schmidt Derivations on Grassmann Algebras

Hasse Schmidt Derivations on Grassmann Algebras Book
Author : Letterio Gatto,Parham Salehyan
Publisher : Springer
Release : 2016-07-08
ISBN : 331931842X
Language : En, Es, Fr & De

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Book Description :

This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Pl├╝cker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.

Algebras Groups and Geometries

Algebras  Groups  and Geometries Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Algebras Groups and Geometries book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Linear Algebra and Geometry

Linear Algebra and Geometry Book
Author : Igor R. Shafarevich,Alexey O. Remizov
Publisher : Springer Science & Business Media
Release : 2012-08-23
ISBN : 3642309941
Language : En, Es, Fr & De

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Book Description :

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.

Notes on Tensor and Exterior Products in Vector Spaces

Notes on Tensor and Exterior Products in Vector Spaces Book
Author : E. C. Thompson
Publisher : Unknown
Release : 1979
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Notes on Tensor and Exterior Products in Vector Spaces book written by E. C. Thompson, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society Book
Author : American Mathematical Society
Publisher : Unknown
Release : 1963
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Bulletin of the American Mathematical Society book written by American Mathematical Society, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Progress of Theoretical Physics

Progress of Theoretical Physics Book
Author : Anonim
Publisher : Unknown
Release : 1990
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Progress of Theoretical Physics book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Lie Groups and Lie Algebras

Lie Groups and Lie Algebras Book
Author : Nicolas Bourbaki
Publisher : Unknown
Release : 1975
ISBN : 9782705658267
Language : En, Es, Fr & De

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Book Description :

Download Lie Groups and Lie Algebras book written by Nicolas Bourbaki, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

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 Book
Author : A. D. Berenstein,A. V. Zelevinsky
Publisher : Unknown
Release : 1990
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Triple Multiplicities for Sl R 1 and Spectrum of the Exterior Algebra of Adjoint Representation book written by A. D. Berenstein,A. V. Zelevinsky, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Quantum Deformations of Algebras and Their Representations

Quantum Deformations of Algebras and Their Representations Book
Author : Anthony Joseph
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Quantum Deformations of Algebras and Their Representations book written by Anthony Joseph, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

International Journal of Mathematics Game Theory and Algebra

International Journal of Mathematics  Game Theory  and Algebra Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download International Journal of Mathematics Game Theory and Algebra book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.