A survey on the spectral theory of nonnegative tensors
A survey on the spectral theory of nonnegative tensors
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DOI：
10.1002/nla.1902
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发表时间：
2013-12-01
影响因子：
4.3
通讯作者：
Zhang, Tan
中科院分区：
文献类型：
--
作者：
Chang, Kungching;Qi, Liqun;Zhang, Tan
本文综述了非负张量谱理论及其应用的最新发展。在简要回顾了张量的基本定义之后，分别研究了张量的H-特征值问题和Z-特征值问题。对于非负张量的H-特征值问题，完整地推广了非负矩阵的Perron-Frobenius理论，而对于Z-特征值问题，则有许多区别并得到了详细的研究。文中还讨论了数值方法。研究了三种应用：高阶马尔可夫链、超图的谱理论和量子纠缠。版权所有(C)2013 John Wiley&Sons，Ltd.
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 (C) 2013 John Wiley & Sons, Ltd.