Exterior Algebras

• Author : Vincent Pavan
• Publisher : Elsevier
• Release : 25 May 2017

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

• Author : Robert B. Gardner
• Publisher : Unknown Publisher
• Release : 27 February 1972

• Author : Juan R. Ruiz-Tolosa,Enrique Castillo
• Publisher : Springer Science & Business Media
• Release : 30 March 2006

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.

• Author : Takeo Yokonuma
• Publisher : American Mathematical Soc.
• Release : 27 February 1992

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

• Author : Takeo Yokonuma
• Publisher : Springer Science & Business
• Release : 27 February 1992

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

• Author : Johan G. F. Belinfante,Bernard Kolman
• Publisher : SIAM
• Release : 01 January 1989

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

• Author : N. Bourbaki
• Publisher : Springer Science & Business Media
• Release : 03 August 1998

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.

• Author : Claude Chevalley
• Publisher : Springer Science & Business Media
• Release : 13 December 1996

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

• Author : Jacques Helmstetter,Artibano Micali
• Publisher : Springer Science & Business Media
• Release : 24 May 2008

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.

• Author : A. D. Berenstein,A. V. Zelevinsky
• Publisher : Unknown Publisher
• Release : 27 February 1990

• Author : Anonim
• Publisher : Unknown Publisher
• Release : 27 February 1999

• Author : Sergei Winitzki
• Publisher : Sergei Winitzki
• Release : 04 January 2010

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

• Author : Bruce Cooperstein
• Publisher : CRC Press
• Release : 19 April 2016

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

• Author : Anonim
• Publisher : Unknown Publisher
• Release : 27 February 1968

• Author : Anonim
• Publisher : Unknown Publisher
• Release : 27 February 2021