1. A survey on the spectral theory of nonnegative tensors.
- Author
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Chang, Kungching, Qi, Liqun, and Zhang, Tan
- Subjects
- *
SPECTRAL theory , *NONNEGATIVE matrices , *TENSOR algebra , *EIGENVALUES , *HYPERGRAPHS , *QUANTUM entanglement , *QUANTUM theory , *MARKOV processes - Abstract
SUMMARY This is a survey paper on the recent development of the spectral theory of nonnegative tensors and its applications. After a brief review of the basic definitions on tensors, the H-eigenvalue problem and the Z-eigenvalue problem for tensors are studied separately. To the H-eigenvalue problem for nonnegative tensors, the whole Perron-Frobenius theory for nonnegative matrices is completely extended, while to the Z-eigenvalue problem, there are many distinctions and are studied carefully in details. Numerical methods are also discussed. Three kinds of applications are studied: higher order Markov chains, spectral theory of hypergraphs, and the quantum entanglement. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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