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Open AccessArticle

New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors

School of mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China
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Mathematics 2018, 6(12), 303; https://doi.org/10.3390/math6120303
Received: 30 September 2018 / Revised: 22 November 2018 / Accepted: 30 November 2018 / Published: 5 December 2018
In this paper, we give a new Z-eigenvalue localization set for Z-eigenvalues of structured fourth order tensors. As applications, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative fourth order tensors is obtained and a new Z-eigenvalue based sufficient condition for the positive definiteness of fourth order tensors is also presented. Finally, numerical examples are given to verify the efficiency of our results. View Full-Text
Keywords: fourth order tensor; bound; nonnegative tensor; Z-eigenvalue; positive definiteness fourth order tensor; bound; nonnegative tensor; Z-eigenvalue; positive definiteness
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He, J.; Liu, Y.; Tian, J.; Zhang, Z. New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors. Mathematics 2018, 6, 303.

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