From Algebraic Structures To Tensors
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From Algebraic Structures To Tensors
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Author : Gérard Favier
language : en
Publisher: John Wiley & Sons
Release Date : 2020-01-02
From Algebraic Structures To Tensors written by Gérard Favier 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 2020-01-02 with Technology & Engineering categories.
Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order.
Introduction To Vectors And Tensors
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Author : Ray M. Bowen
language : en
Publisher: Springer
Release Date : 1976-05-31
Introduction To Vectors And Tensors written by Ray M. Bowen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-05-31 with Mathematics categories.
To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
Tensor Spaces And Numerical Tensor Calculus
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Nature
Release Date : 2019-12-16
Tensor Spaces And Numerical Tensor Calculus written by Wolfgang Hackbusch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.
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.
Tensor Algebra And Tensor Analysis For Engineers
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Author : Mikhail Itskov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-04
Tensor Algebra And Tensor Analysis For Engineers written by Mikhail Itskov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-04 with Technology & Engineering categories.
There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
From Vectors To Tensors
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Author : Juan R. Ruiz-Tolosa
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-29
From Vectors To Tensors written by Juan R. Ruiz-Tolosa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-29 with Computers categories.
This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.
Tensor Analysis
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Author : Liqun Qi
language : en
Publisher: SIAM
Release Date : 2017-04-19
Tensor Analysis written by Liqun Qi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.
Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.
Matrix And Tensor Decompositions In Signal Processing Volume 2
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Author : Gérard Favier
language : en
Publisher: John Wiley & Sons
Release Date : 2021-08-17
Matrix And Tensor Decompositions In Signal Processing Volume 2 written by Gérard Favier 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 2021-08-17 with Technology & Engineering categories.
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.
Tensor Structures And Applications
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Author : Richard Johnson
language : en
Publisher: HiTeX Press
Release Date : 2025-06-20
Tensor Structures And Applications written by Richard Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-20 with Computers categories.
"Tensor Structures and Applications" "Tensor Structures and Applications" offers a comprehensive and rigorous exploration of tensors, guiding the reader from foundational mathematics to advanced, real-world applications. The book opens with a thorough treatment of the mathematical underpinnings, framing tensors as a natural extension of vectors and matrices through multilinear algebra, formal classification by order and type, and detailed conventions for representation and notation. Further foundational chapters bridge these ideas into the realm of differential geometry, introducing the calculus of tensor fields on manifolds, metric tensors, and their indispensable role in Riemannian geometry and general relativity. Building on these theoretical structures, the text presents an in-depth treatment of tensor decompositions, factorization strategies, and the algorithms that power high-dimensional data analysis. Special attention is given to the unique computational challenges posed by tensor methods, covering efficient data storage, parallel and distributed computing, automatic differentiation, and best practices in leading software libraries. These chapters serve both as a roadmap and a toolbox for researchers and practitioners working with complex, high-order data in numerical and machine learning contexts. The latter sections of the book survey an impressive array of contemporary applications, from signal processing and computer vision—where tensors enable sophisticated tasks such as multi-modal filtering and high-dimensional image analysis—to scientific computing, continuum mechanics, quantum information, and engineering simulations. "Tensor Structures and Applications" concludes by charting emerging research directions, including geometric deep learning, topological data analysis, and multiway network modeling, providing readers with both a solid foundation and a forward-looking perspective in this rapidly evolving field.
Tensors And Manifolds
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Author : Robert H. Wasserman
language : en
Publisher: Oxford University Press
Release Date : 2004-05-14
Tensors And Manifolds written by Robert H. Wasserman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-14 with Mathematics categories.
This book is a new edition of "Tensors and Manifolds: With Applications to Mechanics and Relativity" which was published in 1992. It is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, as well as additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.
New Perspectives In Nuclear Structure
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Author : International Spring Seminar on Nuclear Physics 1995, Ravello, Italy
language : en
Publisher: World Scientific
Release Date : 1996
New Perspectives In Nuclear Structure written by International Spring Seminar on Nuclear Physics 1995, Ravello, Italy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Nuclear astrophysics categories.
"This seminar focuses on recent achievements and new goals of nuclear structure in both experiment and theory. Several topics at the forefront of current research in this field are covered by major experts. The main themes are: exotic nuclei; the present role and perspectives of the shell model; modes of excitation in deformed and superdeformed nuclei; and nuclear astrophysics."--Publisher's website.