Tensor Analysis: Spectral Theory and Special Tensors

ISBN-13: 9781611974744 / Angielski / Miękka / 2017 / 319 str.

Liqun Qi;Ziyan Luo

Opis

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory - some of which are nontrivial - have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis is unique in that it is the first book on the spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors, which is covered in a chapter.