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From Algebraic Structures To Tensors

From Algebraic Structures To Tensors
Author: Gérard Favier
Publisher: John Wiley & Sons
ISBN: 1786301547
Size: 26.92 MB
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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.
From Algebraic Structures to Tensors
Language: en
Pages: 318
Authors: Gérard Favier
Categories: Technology & Engineering
Type: BOOK - Published: 2020-01-02 - Publisher: John Wiley & Sons
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
Introduction to Vectors and Tensors
Language: en
Pages: 434
Authors: Ray M. Bowen, Chao-cheng Wang
Categories: Mathematics
Type: BOOK - Published: 1976-05-31 - Publisher: Springer
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,
Introduction to Vectors and Tensors
Language: en
Pages: 242
Authors: Ray M. Bowen, Chao-cheng Wang
Categories: Technology & Engineering
Type: BOOK - Published: 2012-10-20 - Publisher: Springer
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,
The Algebraic Structure of the Tensor of Matter
Language: en
Pages: 266
Authors: Jerzy Plebanski
Categories: Calculus of tensors
Type: BOOK - Published: 1964 - Publisher:
Books about The Algebraic Structure of the Tensor of Matter
Matrix and Tensor Decompositions in Signal Processing
Language: en
Pages: 384
Authors: Gérard Favier
Categories: Technology & Engineering
Type: BOOK - Published: 2021-08-31 - Publisher: John Wiley & Sons
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
Decomposing Matrices, Tensors, and Images
Language: en
Pages: 195
Authors: Elina Robeva
Categories: Technology & Engineering
Type: BOOK - Published: 2016 - Publisher:
In this thesis we apply techniques from algebraic geometry to problems arising from optimization and statistics. In particular, we consider data that takes the form of a matrix, a tensor or an image, and we study how to decompose it so as to find additional and seemingly hidden information about
Probabilities on Algebraic Structures
Language: en
Pages: 218
Authors: Ulf Grenander
Categories: Mathematics
Type: BOOK - Published: 2008-02 - Publisher: Courier Corporation
This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.
Geometry of the Fundamental Interactions
Language: en
Pages: 179
Authors: M. D. Maia
Categories: Science
Type: BOOK - Published: 2011-06-14 - Publisher: Springer Science & Business Media
The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression
Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory
Language: en
Pages: 210
Authors: Vyjayanthi Chari, Jacob Greenstein, Kailash C. Misra, K. N. Raghavan, Sankaran Viswanath
Categories: Mathematics
Type: BOOK - Published: 2013-11-25 - Publisher: American Mathematical Soc.
This volume contains the proceedings of the International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, held August 12-16, 2010, at the National Institute of Advanced Studies, Bangalore, India, and the follow-up conference held May 18-20, 2012, at the University of California, Riverside, CA. It
Tensors of Geophysics for Mavericks and Mongrels
Language: en
Pages: 240
Authors: Frank Hadsell
Categories: Science
Type: BOOK - Published: 1995-01-01 - Publisher: SEG Books
Books about Tensors of Geophysics for Mavericks and Mongrels