Tensor Analysis

The extraordinarily rapid advances made in mathematics since World War II have resulted in analysis becoming an enormous organism spread­ ing in all directions. Gone for good surely are the days of the great French "courses of analysis" which embodied the whole of the "ana­ lytical" knowledge of the times in three volumes-as the classical work of Camille Jordan. Perhaps that is why present-day textbooks of anal­ ysis are disproportionately modest relative to the present state of the art. More: they have "retreated" to the state before Jordan and Goursat. In recent years the scene has been changing rapidly: Jean Dieudon­ ne is offering us his monumentel Elements d'Analyse (10 volumes) written in the spirit of the great French Course d'Analyse. To the best of my knowledge, the present book is the only one of its size: starting from scratch-from rational numbers, to be precise-it goes on to the theory of distributions, direct integrals, analysis on com­ plex manifolds, Kahler manifolds, the theory of sheaves and vector bun­ dles, etc. My objective has been to show the young reader the beauty and wealth of the unsual world of modern mathematical analysis and to show that it has its roots in the great mathematics of the 19th century and mathematical physics. I do know that the young mind eagerly drinks in beautiful and difficult things, rejoicing in the fact that the world is great and teeming with adventure.

The extraordinarily rapid advances made in mathematics since World War II have resulted in analysis becoming an enormous organism spread­ ing in all directions. Gone for good surely are the days of the great French "courses of analysis" which embodied the whole of the "ana­ lytical" knowledge of the times in three volumes-as the classical work of Camille Jordan. Perhaps that is why present-day textbooks of anal­ ysis are disproportionately modest relative to the present state of the art. More: they have "retreated" to the state before Jordan and Goursat. In recent years the scene has been changing rapidly: Jean Dieudon­ ne is offering us his monumentel Elements d'Analyse (10 volumes) written in the spirit of the great French Course d'Analyse. To the best of my knowledge, the present book is the only one of its size: starting from scratch-from rational numbers, to be precise-it goes on to the theory of distributions, direct integrals, analysis on com­ plex manifolds, Kahler manifolds, the theory of sheaves and vector bun­ dles, etc. My objective has been to show the young reader the beauty and wealth of the unsual world of modern mathematical analysis and to show that it has its roots in the great mathematics of the 19th century and mathematical physics. I do know that the young mind eagerly drinks in beautiful and difficult things, rejoicing in the fact that the world is great and teeming with adventure.

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.

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.

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.