Tensor Pdf

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.

Like many other textbooks the present one is based on a lecture course given by the author for master students of the RWTH Aachen University. In spite of a somewhat di?cult matter those students were able to endure and, as far as I know, are still ?ne. I wish the same for the reader of the book. Although the present book can be referred to as a textbook one ?nds only little plain text inside. I tried to explain the matter in a brief way, nevert- lessgoinginto detailwherenecessary.Ialsoavoidedtediousintroductions and lengthy remarks about the signi?cance of one topic or another. A reader - terested in tensor algebra and tensor analysis but preferring, however, words instead of equations can close this book immediately after having read the preface. The reader is assumed to be familiar with the basics of matrix algebra and continuum mechanics and is encouraged to solve at least some of num- ous exercises accompanying every chapter. Having read many other texts on mathematics and mechanics I was always upset vainly looking for solutions to the exercises which seemed to be most interesting for me. For this reason, all the exercises here are supplied with solutions amounting a substantial part of the book. Without doubt, this part facilitates a deeper understanding of the subject. As a research work this book is open for discussion which will certainly contribute to improving the text for further editions. In this sense, I am very gratefulfor comments,suggestionsand constructivecriticismfromthe reader.

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra.

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.