1.

Record Nr.

UNINA9910816024503321

Titolo

Matrices and tensors in signal processing set . Volume 1 From algebraic structures to tensors / / edited by Gerard Favier

Pubbl/distr/stampa

London : , : ISTE : , : Wiley, , 2019

ISBN

9781119681090

111968109X

9781119681113

1119681111

9781119681137

1119681138

Edizione

[1st ed.]

Descrizione fisica

1 online resource

Collana

Digital signal and image processing series ; ; volume 1

Disciplina

512.9

Soggetti

Tensor algebra

Matrices

Algebraic spaces

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Volume 1. From algebraic structures to tensors.

Sommario/riassunto

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.