Multilinear Algebra
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Multilinear Algebra
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Author : Werner H. Greub
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multilinear Algebra written by Werner H. Greub and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Multilinear Algebra
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Author : Werner Greub
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multilinear Algebra written by Werner Greub and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Elements Of Linear And Multilinear Algebra
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Author : John M Erdman
language : en
Publisher: World Scientific
Release Date : 2020-12-22
Elements Of Linear And Multilinear Algebra written by John M Erdman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with Mathematics categories.
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
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Author : Russell Merris
language : en
Publisher: CRC Press
Release Date : 1997-08-20
Multilinear Algebra written by Russell Merris and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-20 with Mathematics categories.
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
Multilinear Algebra
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Author : D. G. Northcott
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-18
Multilinear Algebra written by D. G. Northcott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-18 with Mathematics categories.
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.
Multilinear Algebra
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Author : Werner Hildbert Greub
language : en
Publisher:
Release Date : 1978-01
Multilinear Algebra written by Werner Hildbert Greub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-01 with Algèbre linéaire categories.
Introduction To Vectors And Tensors
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Author : Ray M. Bowen
language : en
Publisher: Springer
Release Date : 1976-05-31
Introduction To Vectors And Tensors written by Ray M. Bowen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-05-31 with Mathematics categories.
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.
Matrix Calculus Kronecker Product And Tensor Product A Practical Approach To Linear Algebra Multilinear Algebra And Tensor Calculus With Software Implementations Third Edition
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Author : Hardy Yorick
language : en
Publisher: World Scientific
Release Date : 2019-04-08
Matrix Calculus Kronecker Product And Tensor Product A Practical Approach To Linear Algebra Multilinear Algebra And Tensor Calculus With Software Implementations Third Edition written by Hardy Yorick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-08 with Mathematics categories.
Our self-contained volume provides an accessible introduction to linear and multilinear algebra as well as tensor calculus. Besides the standard techniques for linear algebra, multilinear algebra and tensor calculus, many advanced topics are included where emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, Hopf algebra, Yang-Baxter relations, computer graphics, fractals, quantum mechanics, quantum computing, entanglement, teleportation and partial trace. All these fields are covered comprehensively.The volume contains many detailed worked-out examples. Each chapter includes useful exercises and supplementary problems. In the last chapter, software implementations are provided for different concepts. The volume is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the third edition are: mutually unbiased bases, Cayley transform, spectral theorem, nonnormal matrices, Gâteaux derivatives and matrices, trace and partial trace, spin coherent states, Clebsch-Gordan series, entanglement, hyperdeterminant, tensor eigenvalue problem, Carleman matrix and Bell matrix, tensor fields and Ricci tensors, and software implementations.
Linear Algebra And Group Representations Multilinear Algebra And Group Representations
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Author : Ronald Shaw
language : en
Publisher:
Release Date : 1982
Linear Algebra And Group Representations Multilinear Algebra And Group Representations written by Ronald Shaw and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Finite Dimensional Multilinear Algebra
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Author : Marvin Marcus
language : en
Publisher:
Release Date : 1973
Finite Dimensional Multilinear Algebra written by Marvin Marcus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algebras, Linear categories.