New eigenvalue inclusion sets for tensors |
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| Authors: | Chaoqian Li Yaotang Li Xu Kong |
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| Affiliation: | 1. School of Mathematics and Statistics, Yunnan University, , Kunming, Yunnan, 650091 China;2. Department of Mathematics, Xi'an Jiaotong University, , Xi'an, 710049 China |
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| Abstract: | Two new eigenvalue inclusion sets for tensors are established. It is proved that the new eigenvalue inclusion sets are tighter than that in Qi's paper “Eigenvalues of a real supersymmetric tensor”. As applications, upper bounds for the spectral radius of a nonnegative tensor are obtained, and it is proved that these upper bounds are sharper than that in Yang's paper “Further results for Perron–Frobenius theorem for nonnegative tensors”. And some sufficient conditions of the positive definiteness for an even‐order real supersymmetric tensor are given. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | tensor eigenvalue nonnegative tensor spectral radius positive definite supersymmetric tensor |
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