Abstract
A Gersgorin-type E-eigenvalue localization set and two Brauer-type E-eigenvalue localization sets for fourth-order tensors are presented. As applications, some sufficient conditions for the positive (semi-)definiteness of fourth-order real symmetric tensors and some upper bounds for the Z-spectral radius of fourth-order weakly symmetric nonnegative tensors are obtained. Finally, numerical examples are given to verify the theoretical results.
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