Tensor-Based Dynamical Systems

Theory and Applications

Can Chen (Autor)

Buch | Hardcover

XV, 106 Seiten

2024 | 2024
Springer International Publishing (Verlag)
978-3-031-54504-7 (ISBN)

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This book provides a comprehensive review on tensor algebra, including tensor products, tensor unfolding, tensor eigenvalues, and tensor decompositions. Tensors are multidimensional arrays generalized from vectors and matrices, which can capture higher-order interactions within multiway data. In addition, tensors have wide applications in many domains such as signal processing, machine learning, and data analysis, and the author explores the role of tensors/tensor algebra in tensor-based dynamical systems where system evolutions are captured through various tensor products. The author provides an overview of existing literature on the topic and aims to inspire readers to learn, develop, and apply the framework of tensor-based dynamical systems.

Can Chen, Ph.D. is an Assistant Professor in the School of Data Science and Society with a second appointment in the Department of Mathematics at the University of North Carolina at Chapel Hill. He received the B.S. degree in Mathematics from the University of California, Irvine in 2016, and the M.S. degree in Electrical and Computer Engineering and the Ph.D. degree in Applied and Interdisciplinary Mathematics from the University of Michigan in 2020 and 2021, respectively. He was a Postdoctoral Research Fellow in the Channing Division of Network Medicine at Brigham and Women's Hospital and Harvard Medical School from 2021 to 2023. His research interests span a diverse range of fields, including control theory, network science, tensor algebra, numerical analysis, data science, machine learning, deep learning, hypergraph learning, data analysis, and computational biology.

Tensors and Tensor Algebra.- Tucker Product Representation.- Einstein Product Representation.- CP/tensor Train Decomposition Representation.- Tensor Vector Product Representation.- Contract Product Representation.- T-product Representation.

Erscheinungsdatum	07.03.2024
Reihe/Serie	Synthesis Lectures on Mathematics & Statistics
Zusatzinfo	XV, 106 p. 19 illus., 17 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Technik
Schlagworte	Control design • Control Theory • Dynamical Systems • Model Reduction • System Identification • Tensor Algebra • tensor decomposition • Tensor Eigenvalues
ISBN-10	3-031-54504-4 / 3031545044
ISBN-13	978-3-031-54504-7 / 9783031545047
Zustand	Neuware