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# Tensor Analysis: Spectral Theory and Special Tensors

#### by Liqun Qi and Ziyan Luo

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2017 / xiv + 305 pages / Softcover / ISBN 978-1-611974-74-4 List Price $84.00 / SIAM Member Price$58.80 / Order Code: OT151

Keywords: tensors, eigenvalues, multilinear algebra, hypergraphs, spectral theory

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.

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: Spectral Theory and Special Tensors 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.

Audience
The intended audience is researchers and graduate students.