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Tensor Eigenvalues and Their Applications

  • Book
  • © 2018

Overview

Authors:
  1. Liqun Qi

    1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, Hong Kong

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  2. Haibin Chen

    1. School of Management Sciences, Qufu Normal University, Rizhao, China

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    You can also search for this author in PubMed   Google Scholar

  3. Yannan Chen

    1. The Hong Kong Polytechnic University, Hong Kong, Hong Kong

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  • Is the first comprehensive book on various applications of eigenvalues of tensors
  • Discusses applied mathematics theoretical topics as well as real-world applications
  • Offers a ready-to-use guide for applied mathematicians and engineers

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 39)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Preliminaries

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 1-7

  3. Multilinear Systems

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 9-47

  4. Hankel Tensor Computation and Exponential Data Fitting

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 49-64

  5. Tensor Complementarity Problems

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 65-134

  6. Tensor Eigenvalue Complementarity Problems

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 135-182

  7. Higher Order Diffusion Tensor Imaging

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 183-206

  8. Third Order Tensors in Physics and Mechanics

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 207-248

  9. Fourth Order Tensors in Physics and Mechanics

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 249-284

  10. Higher Order Tensors in Quantum Physics

    • Liqun Qi, Haibin Chen, Yannan Chen
    Pages 285-311

  11. Back Matter

    Pages 313-329
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Keywords

About this book

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.


Reviews

“This carefully written book is really useful for students, researchers, practitioners, and anybody who is interested in tensors, numerical multilinear algebra, and related subjects. This book will provide a good base for further research on tensor eigenvalue applications in these and some more areas. I definitely recommend this book!” (Guyan Ni, Mathematical Reviews, December, 2018)

Authors and Affiliations

  • Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Liqun Qi

  • School of Management Sciences, Qufu Normal University, Rizhao, China

    Haibin Chen

  • The Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Yannan Chen

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