A survey on the spectral theory of nonnegative tensors | Zendy

Chang Kungching | Zendy; Qi Liqun | Zendy; Zhang Tan | Zendy

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A survey on the spectral theory of nonnegative tensors

Author(s) -

Chang Kungching,

Qi Liqun,

Zhang Tan

Publication year - 2013

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.1902

Subject(s) - eigenvalues and eigenvectors , mathematics , spectral theory , quantum entanglement , markov chain , order (exchange) , spectrum (functional analysis) , pure mathematics , quantum , quantum mechanics , statistics , hilbert space , physics , finance , economics

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.

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