Matrix And Tensor Calculus
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Matrix And Tensor Calculus
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Author : Aristotle D. Michal
language : en
Publisher:
Release Date : 1947
Matrix And Tensor Calculus written by Aristotle D. Michal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with Calculus of tensors categories.
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 : Yorick Hardy
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 Yorick Hardy 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.
Tensor Calculus With Object Oriented Matrices For Numerical Methods In Mechanics And Engineering
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Author : Udo F. Meissner
language : en
Publisher: Springer Nature
Release Date : 2024-10-18
Tensor Calculus With Object Oriented Matrices For Numerical Methods In Mechanics And Engineering written by Udo F. Meissner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-18 with Technology & Engineering categories.
The intension of the book is to synthesize classical matrix and tensor methods with object-oriented software techniques and efficient matrix methods for numerical algorithms. The aim is to establish a coherent methodological framework through which the tensor-based modeling of physical phenomena can be seamlessly applied in numerical algorithms without encountering methodological inconsistencies across different sub-areas, like indexed notation of tensors and two- dimensional matrix algebra in symbolic notation. The key to an effective solution lies in object-oriented numerical structures and software design. The author presents a coherent integration of tensor-based theory through multi-dimensional matrix calculus to object-oriented numeric classes and methods for adequate simulations. The index-based tensor and matrix notation and the object-oriented overloading of standard operators in C++ offers an innovative means to define comparable matrix operations for processing matrix objects of higher order. Typical applications demonstrate the advantages of this unique integration.
Matrices And Tensors In Physics
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Author : A. W. Joshi
language : en
Publisher: New Age International
Release Date : 1995
Matrices And Tensors In Physics written by A. W. Joshi and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The First Part Of This Book Begins With An Introduction To Matrices Through Linear Transformations On Vector Spaces, Followed By A Discussion On The Algebra Of Matrices, Special Matrices, Linear Equations, The Eigenvalue Problem, Bilinear And Quadratic Forms, Kronecker Sum And Product Of Matrices. Other Matrices Which Occur In Physics, Such As The Rotation Matrix, Pauli Spin Matrices And Dirac Matrices, Are Then Presented. A Brief Account Of Infinite Matrices From The Point Of View Of Matrix Formulation Of Quantum Mechanics Is Also Included. The Emphasis In This Part Is On Linear Dependence And Independence Of Vectors And Matrices, Linear Combinations, Independent Parameters Of Various Special Matrices And Such Other Concepts As Help The Student In Obtaining A Clear Understanding Of The Subject. A Simplified Proof Of The Theorem That A Common Set Of Eigenvectors Can Be Found For Two Commuting Matrices Is Given. The Second Part Deals With Cartesian And General Tensors. Many Physical Situations Are Discussed Which Require The Use Of Second And Higher Rank Tensors, Such As Effective Mass Tensor, Moment Of Inertia Tensor, Stress, Strain And Elastic Constants, Piezoelectric Strain Coefficient Tensor, Etc. Einsteins Summation Convention Is Explained In Detail And Common Errors Arising In Its Use Are Pointed Out. Rules For Checking The Correctness Of Tensor Equations Are Given. This Is Followed By Four-Vectors In Special Relativity And Covarient Formulation Of Electrodynamics. This Part Comes To An End With The Concept Of Parallel Displacement Of Vectors In Riemannian Space And Covariant Derivative Of Tensors, Leading To The Curvature Tensors And Its Properties.Appendix I Has Expanded And Two New Appendices Have Been Added In This Edition.
Matrix And Tensor Calculus
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Author : Michal
language : en
Publisher:
Release Date : 1948
Matrix And Tensor Calculus written by Michal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Calculus of tensors categories.
An Introduction To Linear Algebra And Tensors
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Author : M. A. Akivis
language : en
Publisher: Courier Corporation
Release Date : 2012-07-25
An Introduction To Linear Algebra And Tensors written by M. A. Akivis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-25 with Mathematics categories.
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Matrix And Tensor Analysis In Electrical Network Theory
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Author : Stanley Austen Stigant
language : en
Publisher:
Release Date : 1964
Matrix And Tensor Analysis In Electrical Network Theory written by Stanley Austen Stigant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Calculus of tensors categories.
Matrix And Tensor Calculus With Applications To Mechanics Elasticity And Aeronautics Etc
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Author : Aristotle D. MICHAL
language : en
Publisher:
Release Date : 1947
Matrix And Tensor Calculus With Applications To Mechanics Elasticity And Aeronautics Etc written by Aristotle D. MICHAL and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with categories.
Applied Matrix And Tensor Analysis
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Author : John A. Eisele
language : en
Publisher: John Wiley & Sons
Release Date : 1970
Applied Matrix And Tensor Analysis written by John A. Eisele and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Tensor Calculus For Engineers And Physicists
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Author : Emil de Souza Sánchez Filho
language : en
Publisher: Springer
Release Date : 2016-05-20
Tensor Calculus For Engineers And Physicists written by Emil de Souza Sánchez Filho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-20 with Technology & Engineering categories.
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.