Tensor Spaces And Exterior Algebra

Author : Takeo Yokonuma
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 41,6 Mb
Release : 1992
Category : Mathematics
ISBN : 0821827960

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Tensor Spaces and Exterior Algebra by Takeo Yokonuma Pdf

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.

Author : Werner Greub
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394259

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Multilinear Algebra by Werner Greub Pdf

This book is a revised version of the first edition and is intended as a Linear Algebra sequel and companion volume to the fourth edition of (Graduate Texts in Mathematics 23). As before, the terminology and basic results of Linear Algebra are frequently used without refer~nce. In particular, the reader should be familiar with Chapters 1-5 and the first part of Chapter 6 of that book, although other sections are occasionally used. In this new version of Multilinear Algebra, Chapters 1-5 remain essen tially unchanged from the previous edition. Chapter 6 has been completely rewritten and split into three (Chapters 6, 7, and 8). Some of the proofs have been simplified and a substantial amount of new material has been added. This applies particularly to the study of characteristic coefficients and the Pfaffian. The old Chapter 7 remains as it stood, except that it is now Chapter 9. The old Chapter 8 has been suppressed and the material which it con tained (multilinear functions) has been relocated at the end of Chapters 3, 5, and 9. The last two chapters on Clifford algebras and their representations are completely new. In view of the growing importance of Clifford algebras and the relatively few references available, it was felt that these chapters would be useful to both mathematicians and physicists.

Author : Katsumi Nomizu
Publisher : Unknown
Page : 190 pages
File Size : 40,8 Mb
Release : 1961
Category : Calculus of tensors
ISBN : STANFORD:36105031175644

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Vector Spaces and Tensor Algebras by Katsumi Nomizu Pdf

Author : Sergei Winitzki
Publisher : Sergei Winitzki
Page : 286 pages
File Size : 50,8 Mb
Release : 2009-07-30
Category : Science
ISBN : 9781409294962

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Linear Algebra Via Exterior Products by Sergei Winitzki Pdf

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.

Author : E. C. Thompson
Publisher : Unknown
Page : 108 pages
File Size : 47,5 Mb
Release : 1979
Category : Tensor products
ISBN : UOM:39015015600672

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Notes on Tensor and Exterior Products in Vector Spaces by E. C. Thompson Pdf

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 49,5 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

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Tensors: Geometry and Applications by J. M. Landsberg Pdf

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Author : Juan R. Ruiz-Tolosa,Enrique Castillo
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 54,7 Mb
Release : 2005-12-08
Category : Computers
ISBN : 9783540270669

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From Vectors to Tensors by Juan R. Ruiz-Tolosa,Enrique Castillo Pdf

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 : Werner H Greub
Publisher : Unknown
Page : 242 pages
File Size : 55,7 Mb
Release : 1967-01-01
Category : Electronic
ISBN : 3662007967

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Multilinear Algebra. by Werner H Greub Pdf

Author : Hongyu Guo
Publisher : World Scientific Publishing Company
Page : 524 pages
File Size : 45,9 Mb
Release : 2014-04-01
Category : Computers
ISBN : 9789814449359

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Modern Mathematics And Applications In Computer Graphics And Vision by Hongyu Guo Pdf

This book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.

Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 48,6 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031

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What Are Tensors Exactly? by Hongyu Guo Pdf

Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.

Author : Adam Marsh
Publisher : World Scientific
Page : 301 pages
File Size : 55,6 Mb
Release : 2017-11-27
Category : Science
ISBN : 9789813233935

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Mathematics For Physics: An Illustrated Handbook by Adam Marsh Pdf

This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.

Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 44,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193

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Manifolds, Tensors and Forms by Paul Renteln Pdf

Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 54,9 Mb
Release : 2021-11-09
Category : Education
ISBN : 9781470465711

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Algebra: Chapter 0 by Paolo Aluffi Pdf

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Author : P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin
Publisher : CRC Press
Page : 324 pages
File Size : 40,7 Mb
Release : 1997-10-01
Category : Mathematics
ISBN : 9056990497

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Linear Algebra and Geometry by P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin Pdf

This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.

Author : Saunders Mac Lane,Garrett Birkhoff
Publisher : American Mathematical Society
Page : 650 pages
File Size : 40,6 Mb
Release : 2023-10-10
Category : Mathematics
ISBN : 9781470474768

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Algebra by Saunders Mac Lane,Garrett Birkhoff Pdf

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.