Matrix Calculus Kronecker Product And Tensor Product

Author : Hardy Yorick,Steeb Willi-hans
Publisher : World Scientific
Page : 388 pages
File Size : 41,9 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9789811202537

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Matrix Calculus, Kronecker Product And Tensor Product: A Practical Approach To Linear Algebra, Multilinear Algebra And Tensor Calculus With Software Implementations (Third Edition) by Hardy Yorick,Steeb Willi-hans Pdf

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.

Author : Willi-Hans Steeb,Yorick Hardy
Publisher : World Scientific
Page : 323 pages
File Size : 44,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814335317

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Matrix Calculus and Kronecker Product by Willi-Hans Steeb,Yorick Hardy Pdf

This volume examines a variety of philosophical approaches that seek to formulate practical guidelines or norms for human actions and behavior in different areas of society, including politics, cultural traditions, the environment, business management, architecture, and medicine. Written by a team of international authors, this volume features thirteen surveys. It begins with an exploration of ethics in politics and cultural traditions. From genocide to the unequal distribution of wealth, it examines many of the harms that currently affect societies throughout the world and considers a way that those in politics can follow to provide better care for all their populations. Next, the book looks at the relation between ethics and cultural traditions. It features a paper that examines the tension that often exists between the past and the present, with a special focus on the history of India. This volume also considers the idea of a universal system of ethics, presents a practical approach to value-based management in private and public organizations, and examines ethics in medicine. In addition, this volume includes coverage of a new type of ethics called Eco-ethica, proposed by the Japanese philosopher Tomonobu Imamichi, which seeks to answer the question of how men and women can "live better" or "live together with each other" in a systematized, technological age.

Author : Yorick Hardy
Publisher : Unknown
Page : 388 pages
File Size : 41,7 Mb
Release : 2019
Category : Electronic
ISBN : 9811202524

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Matrix Calculus, Kronecker Product and Tensor Product by Yorick Hardy Pdf

Author : Willi-Hans Steeb,Yorick Hardy
Publisher : World Scientific Publishing Company
Page : 324 pages
File Size : 50,5 Mb
Release : 2011-03-24
Category : Mathematics
ISBN : 9789813108073

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Matrix Calculus and Kronecker Product by Willi-Hans Steeb,Yorick Hardy Pdf

This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers. New topics added to the second edition are: braid-like relations, Clebsch–Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product.

Author : Willi-Hans Steeb,Tan Kiat Shi
Publisher : World Scientific
Page : 270 pages
File Size : 55,6 Mb
Release : 1997
Category : Science
ISBN : 9810232411

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Matrix Calculus and Kronecker Product with Applications and C++ Programs by Willi-Hans Steeb,Tan Kiat Shi Pdf

The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-oriented design.

Author : Alexander Graham
Publisher : Courier Dover Publications
Page : 145 pages
File Size : 43,7 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486824178

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Kronecker Products and Matrix Calculus with Applications by Alexander Graham Pdf

Enhanced by many worked examples, problems, and solutions, this in-depth text is suitable for undergraduates and presents a great deal of information previously only available in specialized and hard-to-find texts. 1981 edition.

Author : Jan R. Magnus,Heinz Neudecker
Publisher : John Wiley & Sons
Page : 633 pages
File Size : 42,8 Mb
Release : 2019-03-15
Category : Mathematics
ISBN : 9781119541165

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Matrix Differential Calculus with Applications in Statistics and Econometrics by Jan R. Magnus,Heinz Neudecker Pdf

A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

Author : Dai-Zhan Cheng,Yin Zhao
Publisher : World Scientific
Page : 610 pages
File Size : 48,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814374699

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An Introduction to Semi-tensor Product of Matrices and Its Applications by Dai-Zhan Cheng,Yin Zhao Pdf

A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.

Author : W.-H. Steeb
Publisher : Unknown
Page : 0 pages
File Size : 51,6 Mb
Release : 2011
Category : Kronecker products
ISBN : OCLC:1392375467

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Matrix Calculus and Kronecker Product by W.-H. Steeb Pdf

Author : Wolfgang Hackbusch
Publisher : Springer Nature
Page : 605 pages
File Size : 48,9 Mb
Release : 2019-12-16
Category : Mathematics
ISBN : 9783030355548

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Tensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch Pdf

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Author : M.S. Moonen,Gene H. Golub,B.L. de Moor
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 50,8 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9789401581967

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Linear Algebra for Large Scale and Real-Time Applications by M.S. Moonen,Gene H. Golub,B.L. de Moor Pdf

Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 44,8 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642

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Tensor Calculus for Physics by Dwight E. Neuenschwander Pdf

It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"

Author : Willi-Hans Steeb,Yorick Hardy
Publisher : World Scientific Publishing Company
Page : 568 pages
File Size : 44,5 Mb
Release : 2016-07-14
Category : Mathematics
ISBN : 9789813143814

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Problems and Solutions in Introductory and Advanced Matrix Calculus by Willi-Hans Steeb,Yorick Hardy Pdf

This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics such as spectral theorem, nonnormal matrices and mutually unbiased bases are included. Many of the problems are related to applications for group theory, Lie algebra theory, wavelets, graph theory and matrix-valued differential forms, benefitting physics and engineering students and researchers alike. It also branches out to problems with tensors and the hyperdeterminant. Computer algebra programs in Maxima and SymbolicC++ have also been provided.

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 50,9 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Author : Shayle R. Searle,Andre I. Khuri
Publisher : John Wiley & Sons
Page : 512 pages
File Size : 42,8 Mb
Release : 2017-05-01
Category : Mathematics
ISBN : 9781118935149

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Matrix Algebra Useful for Statistics by Shayle R. Searle,Andre I. Khuri Pdf

A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also: Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices Covers the analysis of balanced linear models using direct products of matrices Analyzes multiresponse linear models where several responses can be of interest Includes extensive use of SAS, MATLAB, and R throughout Contains over 400 examples and exercises to reinforce understanding along with select solutions Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra. THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand. ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.