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: Yorick Hardy

Publisher: World Scientific

Published: 2019-04-08

Total Pages: 388

ISBN-13: 9811202532

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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

Published: 2011

Total Pages: 323

ISBN-13: 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.

Kronecker Products and Matrix Calculus with Applications
Kronecker Products and Matrix Calculus with Applications

Author: Alexander Graham

Publisher: Courier Dover Publications

Published: 2018-06-13

Total Pages: 145

ISBN-13: 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.

An Introduction to Manifolds
An Introduction to Manifolds

Author: Loring W. Tu

Publisher: Springer Science & Business Media

Published: 2010-10-05

Total Pages: 426

ISBN-13: 1441974008

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Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Automated Solution of Differential Equations by the Finite Element Method
Automated Solution of Differential Equations by the Finite Element Method

Author: Anders Logg

Publisher: Springer Science & Business Media

Published: 2012-02-24

Total Pages: 723

ISBN-13: 3642230997

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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Discrete Calculus
Discrete Calculus

Author: Leo J. Grady

Publisher: Springer Science & Business Media

Published: 2010-07-23

Total Pages: 371

ISBN-13: 1849962901

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This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.