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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Publisher : World Scientific
ISBN 13 : 9811202532
Total Pages : 388 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Matrix Calculus, Kronecker Product And Tensor Product: A Practical Approach To Linear Algebra, Multilinear Algebra And Tensor Calculus With Software Implementations (Third Edition) by : Yorick Hardy

Download or read book 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 Yorick Hardy and published by World Scientific. This book was released on 2019-04-08 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Kronecker Products and Matrix Calculus with Applications

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Author :
Publisher : Courier Dover Publications
ISBN 13 : 0486824179
Total Pages : 145 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Kronecker Products and Matrix Calculus with Applications by : Alexander Graham

Download or read book Kronecker Products and Matrix Calculus with Applications written by Alexander Graham and published by Courier Dover Publications. This book was released on 2018-06-13 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Differential Calculus with Applications in Statistics and Econometrics

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Publisher : John Wiley & Sons
ISBN 13 : 1119541166
Total Pages : 660 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Matrix Differential Calculus with Applications in Statistics and Econometrics by : Jan R. Magnus

Download or read book Matrix Differential Calculus with Applications in Statistics and Econometrics written by Jan R. Magnus and published by John Wiley & Sons. This book was released on 2019-03-15 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Calculus And Kronecker Product: A Practical Approach To Linear And Multilinear Algebra (2nd Edition)

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Publisher : World Scientific Publishing Company
ISBN 13 : 981310807X
Total Pages : 323 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Matrix Calculus And Kronecker Product: A Practical Approach To Linear And Multilinear Algebra (2nd Edition) by : Willi-hans Steeb

Download or read book Matrix Calculus And Kronecker Product: A Practical Approach To Linear And Multilinear Algebra (2nd Edition) written by Willi-hans Steeb and published by World Scientific Publishing Company. This book was released on 2011-03-24 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Calculus and Kronecker Product with Applications and C++ Programs

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Publisher : World Scientific
ISBN 13 : 9789810232412
Total Pages : 270 pages
Book Rating : 4.2/5 (324 download)

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Book Synopsis Matrix Calculus and Kronecker Product with Applications and C++ Programs by : Willi-Hans Steeb

Download or read book Matrix Calculus and Kronecker Product with Applications and C++ Programs written by Willi-Hans Steeb and published by World Scientific. This book was released on 1997 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tensor Spaces and Numerical Tensor Calculus

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Publisher : Springer Nature
ISBN 13 : 3030355543
Total Pages : 622 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : Wolfgang Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Nature. This book was released on 2019-12-16 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Algebra for Large Scale and Real-Time Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9401581967
Total Pages : 434 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Linear Algebra for Large Scale and Real-Time Applications by : M.S. Moonen

Download or read book Linear Algebra for Large Scale and Real-Time Applications written by M.S. Moonen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992

Tensor Categories

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Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tensor Methods in Statistics

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Publisher : Courier Dover Publications
ISBN 13 : 0486832694
Total Pages : 308 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Tensor Methods in Statistics by : Peter McCullagh

Download or read book Tensor Methods in Statistics written by Peter McCullagh and published by Courier Dover Publications. This book was released on 2018-07-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.

Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub

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Publisher : World Scientific
ISBN 13 : 9814469556
Total Pages : 604 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub by : Vadim Olshevsky

Download or read book Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub written by Vadim Olshevsky and published by World Scientific. This book was released on 2010-04-05 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.

Tensor Spaces and Numerical Tensor Calculus

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Publisher : Springer Science & Business Media
ISBN 13 : 3642280277
Total Pages : 525 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : Wolfgang Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2012-02-23 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d 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. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. ​

Nonhomogeneous Matrix Products

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Publisher : World Scientific
ISBN 13 : 9810246285
Total Pages : 236 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Nonhomogeneous Matrix Products by : D. J. Hartfiel

Download or read book Nonhomogeneous Matrix Products written by D. J. Hartfiel and published by World Scientific. This book was released on 2002 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Puts together much of the basic work on infinite products of matrices, providing a primary source for such work.

Matrix and Tensor Decompositions in Signal Processing, Volume 2

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Publisher : John Wiley & Sons
ISBN 13 : 1119700965
Total Pages : 386 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Matrix and Tensor Decompositions in Signal Processing, Volume 2 by : Gérard Favier

Download or read book Matrix and Tensor Decompositions in Signal Processing, Volume 2 written by Gérard Favier and published by John Wiley & Sons. This book was released on 2021-08-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.

Matrix Methods And Fractional Calculus

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Publisher : World Scientific
ISBN 13 : 9813227540
Total Pages : 291 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Matrix Methods And Fractional Calculus by : Arak M Mathai

Download or read book Matrix Methods And Fractional Calculus written by Arak M Mathai and published by World Scientific. This book was released on 2017-11-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus in terms of mathematics and statistics and its applications to problems in natural sciences is NOT yet part of university teaching curricula. This book is one attempt to provide an approach to include topics of fractional calculus into university curricula. Additionally the material is useful for people who do research work in the areas of special functions, fractional calculus, applications of fractional calculus, and mathematical statistics.

Introduction to Matrix Analysis and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3319041509
Total Pages : 337 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Introduction to Matrix Analysis and Applications by : Fumio Hiai

Download or read book Introduction to Matrix Analysis and Applications written by Fumio Hiai and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.

Numerical Linear Algebra and Matrix Factorizations

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Publisher : Springer Nature
ISBN 13 : 3030364682
Total Pages : 376 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Numerical Linear Algebra and Matrix Factorizations by : Tom Lyche

Download or read book Numerical Linear Algebra and Matrix Factorizations written by Tom Lyche and published by Springer Nature. This book was released on 2020-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

Generalized Vectorization, Cross-Products, and Matrix Calculus

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Publisher : Cambridge University Press
ISBN 13 : 1107032008
Total Pages : 281 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Generalized Vectorization, Cross-Products, and Matrix Calculus by : Darrell A. Turkington

Download or read book Generalized Vectorization, Cross-Products, and Matrix Calculus written by Darrell A. Turkington and published by Cambridge University Press. This book was released on 2013-02-11 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the mathematics behind matrix calculus and the applications of matrix calculus in statistics and econometrics.