Author : Werner H Greub
Publisher : Unknown
Page : 242 pages
File Size : 47,9 Mb
Release : 1967-01-01
Category : Electronic
ISBN : 3662007967
Multilinear Algebra.
Werner H Greub
Multilinear Algebra
Multilinear Algebra Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Multilinear Algebra book. This book definitely worth reading, it is an incredibly well-written.
Multilinear Algebra
Russell Merris
Author : Russell Merris
Publisher : CRC Press
Page : 341 pages
File Size : 47,8 Mb
Release : 1997-08-20
Category : Mathematics
ISBN : 9781498714907
Multilinear Algebra by Russell Merris Pdf
The prototypical multilinear operation is multiplication. Indeed, every multilinear mapping can be factored through a tensor product. Apart from its intrinsic interest, the tensor product is of fundamental importance in a variety of disciplines, ranging from matrix inequalities and group representation theory, to the combinatorics of symmetric func
Elements Of Linear And Multilinear Algebra
John M Erdman
Author : John M Erdman
Publisher : World Scientific
Page : 234 pages
File Size : 54,9 Mb
Release : 2020-12-22
Category : Mathematics
ISBN : 9789811222740
Elements Of Linear And Multilinear Algebra by John M Erdman Pdf
This set of notes is an activity-oriented introduction to linear and multilinear algebra. The great majority of the most elementary results in these subjects are straightforward and can be verified by the thoughtful student. Indeed, that is the main point of these notes — to convince the beginner that the subject is accessible. In the material that follows there are numerous indicators that suggest activity on the part of the reader: words such as 'proposition', 'example', 'theorem', 'exercise', and 'corollary', if not followed by a proof (and proofs here are very rare) or a reference to a proof, are invitations to verify the assertions made.These notes are intended to accompany an (academic) year-long course at the advanced undergraduate or beginning graduate level. (With judicious pruning most of the material can be covered in a two-term sequence.) The text is also suitable for a lecture-style class, the instructor proving some of the results while leaving others as exercises for the students.This book has tried to keep the facts about vector spaces and those about inner product spaces separate. Many beginning linear algebra texts conflate the material on these two vastly different subjects.
Multilinear Algebra
Russell Merris
Author : Russell Merris
Publisher : CRC Press
Page : 344 pages
File Size : 48,8 Mb
Release : 1997-08-20
Category : Mathematics
ISBN : 9056990780
Multilinear Algebra by Russell Merris Pdf
The prototypical multilinear operation is multiplication. Indeed, every multilinear mapping can be factored through a tensor product. Apart from its intrinsic interest, the tensor product is of fundamental importance in a variety of disciplines, ranging from matrix inequalities and group representation theory, to the combinatorics of symmetric functions, and all these subjects appear in this book. Another attraction of multilinear algebra lies in its power to unify such seemingly diverse topics. This is done in the final chapter by means of the rational representations of the full linear group. Arising as characters of these representations, the classical Schur polynomials are one of the keys to unification. Prerequisites for the book are minimized by self-contained introductions in the early chapters. Throughout the text, some of the easier proofs are left to the exercises, and some of the more difficult ones to the references.
Multilinear Algebra
Werner H. Greub
Author : Werner H. Greub
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662007952
Multilinear Algebra by Werner H. Greub Pdf
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.
Manifolds, Tensors and Forms
Paul Renteln
Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 46,8 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193
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.
Algebra: Chapter 0
Paolo Aluffi
Author : Paolo Aluffi
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 51,8 Mb
Release : 2021-11-09
Category : Education
ISBN : 9781470465711
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.
Tensors: Geometry and Applications
J. M. Landsberg
Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 49,7 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079
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.
Introduction to Vectors and Tensors
Ray M. Bowen,Chao-cheng Wang
Author : Ray M. Bowen,Chao-cheng Wang
Publisher : Springer
Page : 224 pages
File Size : 49,7 Mb
Release : 1976-05-31
Category : Mathematics
ISBN : UOM:39015017127955
Introduction to Vectors and Tensors by Ray M. Bowen,Chao-cheng Wang Pdf
To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
Multilinear Algebra
D. G. Northcott
Author : D. G. Northcott
Publisher : Cambridge University Press
Page : 0 pages
File Size : 53,5 Mb
Release : 2009-01-18
Category : Mathematics
ISBN : 0521090601
Multilinear Algebra by D. G. Northcott Pdf
Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion. The aim of this book is to provide a readable and systematic account of multilinear algebra at a level suitable for graduate students. Professor Northcott gives a thorough treatment of topics such as tensor, exterior, Grassmann, Hopf and co-algebras and ends each chapter with a section entitled 'Comments and Exercises'. The comments contain convenient summaries and discussion of the content whilst the exercises provide an opportunity to test understanding and add extra material. Complete solutions are provided for those exercises that are particularly important or used later in the book. The volume as a whole is based on advanced lectures given by the author at the University of Sheffield.
Linear Algebra Done Right
Sheldon Axler
Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 46,8 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590
Linear Algebra Done Right by Sheldon Axler Pdf
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Tensor Analysis on Manifolds
Richard L. Bishop,Samuel I. Goldberg
Author : Richard L. Bishop,Samuel I. Goldberg
Publisher : Courier Corporation
Page : 288 pages
File Size : 44,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139234
Tensor Analysis on Manifolds by Richard L. Bishop,Samuel I. Goldberg Pdf
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Linear and Multilinear Algebra and Function Spaces
A. Bourhim,J. Mashreghi,L. Oubbi,Z. Abdelali
Author : A. Bourhim,J. Mashreghi,L. Oubbi,Z. Abdelali
Publisher : American Mathematical Soc.
Page : 213 pages
File Size : 46,5 Mb
Release : 2020-05-05
Category : Education
ISBN : 9781470446932
Linear and Multilinear Algebra and Function Spaces by A. Bourhim,J. Mashreghi,L. Oubbi,Z. Abdelali Pdf
This volume contains the proceedings of the International Conference on Algebra and Related Topics, held from July 2–5, 2018, at Mohammed V University, Rabat, Morocco. Linear reserver problems demand the characterization of linear maps between algebras that leave invariant certain properties or certain subsets or relations. One of the most intractable unsolved problems is Kaplansky's conjecture: every surjective unital invertibility preserving linear map between two semisimple Banach algebras is a Jordan homomorphism. Recently, there has been an upsurge of interest in nonlinear preservers, where the maps studied are no longer assumed linear but instead a weak algebraic condition is somehow involved through the preserving property. This volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on C ∗ C∗-algebras, advertible complete algebras, and Gelfand-Mazur algebras. The volume also contains a survey on recent progress on local spectrum-preserving maps. Several articles in the volume present results about weighted spaces and algebras of holomorphic or harmonic functions, including biduality in weighted spaces of analytic functions, interpolation in the analytic Wiener algebra, and weighted composition operators on non-locally convex weighted spaces.
Introduction to Linear and Matrix Algebra
Nathaniel Johnston
Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 44,5 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119
Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
Multilinear Algebra
Werner Greub
Author : Werner Greub
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394259
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.