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Kronecker Products and Matrix Calculus with Applications

Kronecker Products and Matrix Calculus with Applications
Author: Alexander Graham
Publisher: Courier Dover Publications
Total Pages: 145
Release: 2018-06-13
Genre: Mathematics
ISBN: 0486824179
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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 Calculus and Kronecker Product

Matrix Calculus and Kronecker Product
Author: Willi-Hans Steeb
Publisher: World Scientific
Total Pages: 323
Release: 2011
Genre: Mathematics
ISBN: 9814335312
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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.

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

Matrix Calculus and Kronecker Product with Applications and C++ Programs
Author: Willi-Hans Steeb
Publisher: World Scientific
Total Pages: 270
Release: 1997
Genre: Science
ISBN: 9789810232412
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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.

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

Matrix Calculus, Kronecker Product And Tensor Product: A Practical Approach To Linear Algebra, Multilinear Algebra And Tensor Calculus With Software Implementations (Third Edition)
Author: Hardy Yorick
Publisher: World Scientific
Total Pages: 388
Release: 2019-04-08
Genre: Mathematics
ISBN: 9811202532
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Download Matrix Calculus, Kronecker Product And Tensor Product: A Practical Approach To Linear Algebra, Multilinear Algebra And Tensor Calculus With Software Implementations (Third Edition) Book in PDF, ePub and Kindle

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.

Matrix Calculus and Kronecker Product

Matrix Calculus and Kronecker Product
Author: Willi-Hans Steeb
Publisher: World Scientific Publishing Company
Total Pages: 324
Release: 2011-03-24
Genre: Mathematics
ISBN: 981310807X
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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 Differential Calculus with Applications in Statistics and Econometrics

Matrix Differential Calculus with Applications in Statistics and Econometrics
Author: Jan R. Magnus
Publisher: John Wiley & Sons
Total Pages: 633
Release: 2019-03-15
Genre: Mathematics
ISBN: 1119541166
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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.

Problems and Solutions in Introductory and Advanced Matrix Calculus

Problems and Solutions in Introductory and Advanced Matrix Calculus
Author: Willi-Hans Steeb
Publisher: World Scientific Publishing Company
Total Pages: 568
Release: 2016-07-14
Genre: Mathematics
ISBN: 9813143819
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Download Problems and Solutions in Introductory and Advanced Matrix Calculus Book in PDF, ePub and Kindle

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.

Sensitivity Analysis: Matrix Methods in Demography and Ecology

Sensitivity Analysis: Matrix Methods in Demography and Ecology
Author: Hal Caswell
Publisher: Springer
Total Pages: 308
Release: 2019-04-02
Genre: Social Science
ISBN: 3030105342
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Download Sensitivity Analysis: Matrix Methods in Demography and Ecology Book in PDF, ePub and Kindle

This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.