Tensor Analysis : Spectral Theory and Special Tensors

Qi, Liqun/ Luo, Ziyan

Society for Industrial & Applied Mathematics,U.S.（2017/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 319 p.
• 言語 ENG
• 商品コード 9781611974744
• DDC分類 515.63

Full Description

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.

Contents

List of Figures.
List of Algorithms.
Preface.
Chapter 1: Introduction.
Chapter 2: Eigenvalues of Tensors.
Chapter 3: Nonnegative Tensors.
Chapter 4: Spectral Hypergraph Theory via Tensors.
Chapter 5: Positive Semidefinite Tensors.
Chapter 6: Completely Positive Tensors and Copositive Tensors.
Bibliography.
Index.