Description
Book SynopsisTensors, 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.
Table of 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.
