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Tensor-Based Dynamical Systems

Theory and Applications

  • Book
  • © 2024

Overview

Authors:
  1. Can Chen

    1. School of Data Science and Society and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, USA

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  • Offers a comprehensive review on tensor algebra
  • Introduces tensor-based dynamical systems and explores the role of tensor algebra in these systems
  • Provides real-world interdisciplinary applications from biology, engineering, and physics

Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Tensor Preliminaries

    • Can Chen
    Pages 1-24

  3. Tucker Product-Based Dynamical Systems

    • Can Chen
    Pages 25-37

  4. Einstein Product-Based Dynamical Systems

    • Can Chen
    Pages 39-57

  5. Tensor Vector Product-Based Dynamical Systems

    • Can Chen
    Pages 59-83

  6. Contracted Product-Based Dynamical Systems

    • Can Chen
    Pages 85-96

  7. t-Product-Based Dynamical Systems

    • Can Chen
    Pages 97-106
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Keywords

About this book

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.



Authors and Affiliations

  • School of Data Science and Society and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, USA

    Can Chen

About the author

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.

Bibliographic Information

  • Book Title: Tensor-Based Dynamical Systems

  • Book Subtitle: Theory and Applications

  • Authors: Can Chen

  • Series Title: Synthesis Lectures on Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-031-54505-4

  • Publisher: Springer Cham

  • eBook Packages: Synthesis Collection of Technology (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Hardcover ISBN: 978-3-031-54504-7Published: 05 March 2024

  • Softcover ISBN: 978-3-031-54507-8Due: 15 April 2024

  • eBook ISBN: 978-3-031-54505-4Published: 04 March 2024

  • Series ISSN: 1938-1743

  • Series E-ISSN: 1938-1751

  • Edition Number: 1

  • Number of Pages: XV, 106

  • Number of Illustrations: 2 b/w illustrations, 17 illustrations in colour

  • Topics: Complexity, Control and Systems Theory, Algebra, Linear Algebra

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