Z-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Tensors

摘要

New Z-eigenvalue localization sets for Z-eigenvalues of fourth-order tensors are given. As applications, sharper upper bounds for the Z-spectral radius of weakly symmetric nonnegative fourth-order tensors are obtained. Some Gershgorin-type results for Z-eigenvalues of structured fourth-order tensors are obtained. Then, some Z-eigenvalues-based sufficient conditions for the positive definiteness of fourth-order tensors are also presented. Finally, numerical examples are given to verify the efficiency of our results.