Tensor Eigenvalues and Their Applications

Description

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. Front Matter ....Pages i-xiii Preliminaries (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 1-7 Multilinear Systems (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 9-47 Hankel Tensor Computation and Exponential Data Fitting (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 49-64 Tensor Complementarity Problems (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 65-134 Tensor Eigenvalue Complementarity Problems (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 135-182 Higher Order Diffusion Tensor Imaging (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 183-206 Third Order Tensors in Physics and Mechanics (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 207-248 Fourth Order Tensors in Physics and Mechanics (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 249-284 Higher Order Tensors in Quantum Physics (Liqun Qi, Haibin Chen, Yannan Chen)....Pages 285-311 Back Matter ....Pages 313-329