Exterior Algebras Book

Exterior Algebras

  • Author : Vincent Pavan
  • Publisher : Elsevier
  • Release Date : 2017-05-25
  • Genre: Mathematics
  • Pages : 208
  • ISBN 10 : 9780081023488

Exterior Algebras Excerpt :

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 Book

Tensor Spaces and Exterior Algebra

  • Author : Takeo Yokonuma
  • Publisher : American Mathematical Soc.
  • Release Date : 1992
  • Genre: Multilinear algebra
  • Pages : 148
  • ISBN 10 : 0821827960

Tensor Spaces and Exterior Algebra Excerpt :

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.

Linear Algebra Via Exterior Products Book
Score: 4
From 1 Ratings

Linear Algebra Via Exterior Products

  • Author : Sergei Winitzki
  • Publisher : Sergei Winitzki
  • Release Date : 2009-07-30
  • Genre: Science
  • Pages : 286
  • ISBN 10 : 9781409294962

Linear Algebra Via Exterior Products Excerpt :

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 Book

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

  • Author : Johan G. F. Belinfante
  • Publisher : SIAM
  • Release Date : 1989-01-01
  • Genre: Mathematics
  • Pages : 175
  • ISBN 10 : 1611971330

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

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 Book
Score: 5
From 1 Ratings

Algebra I

  • Author : N. Bourbaki
  • Publisher : Springer Science & Business Media
  • Release Date : 1998-08-03
  • Genre: Mathematics
  • Pages : 750
  • ISBN 10 : 3540642439

Algebra I Excerpt :

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.

From Vectors to Tensors Book

From Vectors to Tensors

  • Author : Juan R. Ruiz-Tolosa
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-03-30
  • Genre: Computers
  • Pages : 670
  • ISBN 10 : 9783540270669

From Vectors to Tensors Excerpt :

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.

Clifford Algebras and Spinor Structures Book

Clifford Algebras and Spinor Structures

  • Author : Rafal Ablamowicz
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Mathematics
  • Pages : 425
  • ISBN 10 : 9789401584227

Clifford Algebras and Spinor Structures Excerpt :

This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.

Fundamental Concepts of Algebra Book

Fundamental Concepts of Algebra

  • Author : Anonim
  • Publisher : Academic Press
  • Release Date : 1957-01-01
  • Genre: Mathematics
  • Pages : 240
  • ISBN 10 : 0080873154

Fundamental Concepts of Algebra Excerpt :

Fundamental Concepts of Algebra

Algebras  Rings and Modules Book

Algebras Rings and Modules

  • Author : Michiel Hazewinkel
  • Publisher : Springer Science & Business Media
  • Release Date : 2007
  • Genre: Modules (Algebra)
  • Pages : 405
  • ISBN 10 : 9781402051401

Algebras Rings and Modules Excerpt :

Handbook of Mathematics Book

Handbook of Mathematics

  • Author : Thierry Vialar
  • Publisher : BoD - Books on Demand
  • Release Date : 2016-12-07
  • Genre: Mathematics
  • Pages : 1134
  • ISBN 10 : 9782955199008

Handbook of Mathematics Excerpt :

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 are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Clifford Algebras and Lie Theory Book

Clifford Algebras and Lie Theory

  • Author : Eckhard Meinrenken
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-02-28
  • Genre: Mathematics
  • Pages : 321
  • ISBN 10 : 9783642362163

Clifford Algebras and Lie Theory Excerpt :

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–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.

Abstract Algebra Book

Abstract Algebra

  • Author : Pierre Antoine Grillet
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-07-21
  • Genre: Mathematics
  • Pages : 674
  • ISBN 10 : 9780387715681

Abstract Algebra Excerpt :

A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories.

Clifford Algebras and Spinors Book

Clifford Algebras and Spinors

  • Author : Pertti Lounesto
  • Publisher : Cambridge University Press
  • Release Date : 2001-05-03
  • Genre: Mathematics
  • Pages : 352
  • ISBN 10 : 9780521005517

Clifford Algebras and Spinors Excerpt :

In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The initial chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This book also gives the first comprehensive survey of recent research on Clifford algebras. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the analytic side, Brauer-Wall groups and Witt rings are discussed, and Caucy's integral formula is generalized to higher dimensions.

Clifford Algebras with Numeric and Symbolic Computations Book

Clifford Algebras with Numeric and Symbolic Computations

  • Author : Rafal Ablamowicz
  • Publisher : Springer Science & Business Media
  • Release Date : 1996-08-01
  • Genre: Mathematics
  • Pages : 348
  • ISBN 10 : 0817639071

Clifford Algebras with Numeric and Symbolic Computations Excerpt :

This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.