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New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors

Author

Listed:
  • Jun He

    (School of mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China)

  • Yanmin Liu

    (School of mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China)

  • Junkang Tian

    (School of mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China)

  • Zhuanzhou Zhang

    (School of mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, China)

Abstract

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.

Suggested Citation

  • Jun He & Yanmin Liu & Junkang Tian & Zhuanzhou Zhang, 2018. "New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors," Mathematics, MDPI, vol. 6(12), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:303-:d:187938
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