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Author : A. W. Joshi
Publisher : Unknown
Page : 289 pages
File Size : 52,5 Mb
Release : 1984
Category : Calculus of tensors
ISBN : 0852264380
Author : George Garfield Hall
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 1963
Category : Calculus of tensors
ISBN : UOM:39015003438473
Author : A. W. Joshi
Publisher : New Age International
Page : 364 pages
File Size : 54,5 Mb
Release : 1995
Category : Mathematics
ISBN : 8122405630
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.
Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 47,5 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642
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 : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 40,7 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author : John A. Eisele,Robert M. Mason
Publisher : John Wiley & Sons
Page : 360 pages
File Size : 55,5 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015623088
Author : J D Renton
Publisher : Elsevier
Page : 212 pages
File Size : 53,7 Mb
Release : 2002-12-30
Category : Science
ISBN : 9780857099587
This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987 Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approach Uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis
Author : Gérard Favier
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 45,9 Mb
Release : 2021-08-17
Category : Technology & Engineering
ISBN : 9781119700968
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.
Author : Simone Malacrida
Publisher : BookRix
Page : 78 pages
File Size : 41,5 Mb
Release : 2023-04-18
Category : Mathematics
ISBN : 9783755439417
The theoretical assumptions of the following mathematical topics are presented in this book: vectors and vector calculus matrices and matrix calculus vector and matrix spaces mathematics and tensor calculus
Author : J. F. Nye
Publisher : Oxford University Press
Page : 356 pages
File Size : 51,8 Mb
Release : 1985
Category : Mathematics
ISBN : 0198511655
First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
Author : Panagiotis Symeonidis,Andreas Zioupos
Publisher : Springer
Page : 102 pages
File Size : 54,8 Mb
Release : 2017-01-29
Category : Computers
ISBN : 9783319413570
This book presents the algorithms used to provide recommendations by exploiting matrix factorization and tensor decomposition techniques. It highlights well-known decomposition methods for recommender systems, such as Singular Value Decomposition (SVD), UV-decomposition, Non-negative Matrix Factorization (NMF), etc. and describes in detail the pros and cons of each method for matrices and tensors. This book provides a detailed theoretical mathematical background of matrix/tensor factorization techniques and a step-by-step analysis of each method on the basis of an integrated toy example that runs throughout all its chapters and helps the reader to understand the key differences among methods. It also contains two chapters, where different matrix and tensor methods are compared experimentally on real data sets, such as Epinions, GeoSocialRec, Last.fm, BibSonomy, etc. and provides further insights into the advantages and disadvantages of each method. The book offers a rich blend of theory and practice, making it suitable for students, researchers and practitioners interested in both recommenders and factorization methods. Lecturers can also use it for classes on data mining, recommender systems and dimensionality reduction methods.
Author : M. A. Akivis,V. V. Goldberg
Publisher : Courier Corporation
Page : 192 pages
File Size : 47,5 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9780486148786
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.
Author : Hardy Yorick,Steeb Willi-hans
Publisher : World Scientific
Page : 388 pages
File Size : 41,8 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9789811202537
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 : Chris Albon
Publisher : "O'Reilly Media, Inc."
Page : 305 pages
File Size : 49,6 Mb
Release : 2018-03-09
Category : Computers
ISBN : 9781491989333
This practical guide provides nearly 200 self-contained recipes to help you solve machine learning challenges you may encounter in your daily work. If you’re comfortable with Python and its libraries, including pandas and scikit-learn, you’ll be able to address specific problems such as loading data, handling text or numerical data, model selection, and dimensionality reduction and many other topics. Each recipe includes code that you can copy and paste into a toy dataset to ensure that it actually works. From there, you can insert, combine, or adapt the code to help construct your application. Recipes also include a discussion that explains the solution and provides meaningful context. This cookbook takes you beyond theory and concepts by providing the nuts and bolts you need to construct working machine learning applications. You’ll find recipes for: Vectors, matrices, and arrays Handling numerical and categorical data, text, images, and dates and times Dimensionality reduction using feature extraction or feature selection Model evaluation and selection Linear and logical regression, trees and forests, and k-nearest neighbors Support vector machines (SVM), naïve Bayes, clustering, and neural networks Saving and loading trained models
Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 54,8 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.