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From Algebraic Structures to Tensors

2020-01-02 Technology & Engineering
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Release : 2020-01-02
Genre : Technology & Engineering
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Book Rating : 547/5 ( reviews)

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Book Synopsis From Algebraic Structures to Tensors by : Gérard Favier

Download or read book From Algebraic Structures to Tensors written by Gérard Favier. This book was released on 2020-01-02. Available in PDF, EPUB and Kindle. Book excerpt: 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

1976-05-31 Mathematics
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Release : 1976-05-31
Genre : Mathematics
Kind : eBook
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Book Synopsis Introduction to Vectors and Tensors by : Ray M. Bowen

Download or read book Introduction to Vectors and Tensors written by Ray M. Bowen. This book was released on 1976-05-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Vectors and Tensors

2012-10-20 Technology & Engineering
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Release : 2012-10-20
Genre : Technology & Engineering
Kind : eBook
Book Rating : 688/5 ( reviews)

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Book Synopsis Introduction to Vectors and Tensors by : Ray M. Bowen

Download or read book Introduction to Vectors and Tensors written by Ray M. Bowen. This book was released on 2012-10-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Vectors and Tensors

1976-05-31 Technology & Engineering
Download Introduction to Vectors and Tensors PDF Online Free

Author :
Release : 1976-05-31
Genre : Technology & Engineering
Kind : eBook
Book Rating : 088/5 ( reviews)

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Book Synopsis Introduction to Vectors and Tensors by : Ray M. Bowen

Download or read book Introduction to Vectors and Tensors written by Ray M. Bowen. This book was released on 1976-05-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Algebra: Tensor Products

Mathematics
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Genre : Mathematics
Kind : eBook
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Book Synopsis Abstract Algebra: Tensor Products by : N.B. Singh

Download or read book Abstract Algebra: Tensor Products written by N.B. Singh. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: "Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics.

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