Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25107
Title: A survey on the spectral theory of nonnegative tensors
Authors: Chang, K
Qi, L 
Zhang, T
Keywords: Eigenvalues for tensors
High order Markov chain
Perron-Frobenius theorem
Issue Date: 2013
Publisher: John Wiley & Sons
Source: Numerical linear algebra with applications, 2013, v. 20, no. 6, p. 891-912 How to cite?
Journal: Numerical linear algebra with applications 
Abstract: 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.
URI: http://hdl.handle.net/10397/25107
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.1902
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