Tensor-Based Dynamical Systems: Theory and Applications

by Can Chen

Overview

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.

Product Details

ISBN-13:	9783031545054
Publisher:	Springer-Verlag New York, LLC
Publication date:	03/04/2024
Series:	Synthesis Lectures on Mathematics & Statistics
Sold by:	Barnes & Noble
Format:	eBook
File size:	11 MB
Note:	This product may take a few minutes to download.

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.

Table of Contents

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.