SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 4

A special cone construction and its connections to structured tensors and their spectra

Vehbi Emrah PAKSOY
Pages
1222–1237
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We obtain an inequality for the spectral radius of certain tensors when theorder m is odd.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a specialcondition, and we study its relations to structured tensors such as M-tensors and H-tensors.
📊
Key Findings & Data:We also investigate itsapplications to spectra of certain Z-tensors.
💡
Conclusion & Impact:We obtain an inequality for the spectral radius of certain tensors when theorder m is odd.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a specialcondition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate itsapplications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when theorder m is odd.

🔖

Cite This Article

PAKSOY, V. E. (2022). A special cone construction and its connections to structured tensors and their spectra. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 4, 1222–1237. https://ajindex.com/articles/608805

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Chang H, Paksoy VE, Zhang F. Polytopes of stochastic tensors. Annals of Functional Analysis 2016; 7: 386-393
  2. Che M, Bu C, Qi L, Wei Y. Nonnegative tensors revisited: plane stochastic tensors. Linear and Multilinear Algebra 2018; 67: 1364-1391
  3. Che M, Wei Y. Theory and Computation of Complex Tensors and its Applications, Springer, 2020 [4] Chen H, Li G, Qi L. SOS tensor decomposition: Theory and applications. Communications in Mathematical Sciences 2016; 14: 2073- 2100
  4. Ding W, Qi L, Wei Y. M- tensors and nonsingular M-tensors. Linear Algebra and Applications 2013; 439: 3264-3278
  5. Dow SJ, Gibson PM. Permanents of d-dimensional matrices. Linear Algebra and Applications 1987; 90: 133-145
  6. Friedlands S, Gaubert S, Han L. Perron Frobenius theorem for nonnegative multilinear forms and extensions. Linear Algebra and Applications 013; 438: 738-749
  7. Hu S, Qi L, Xie J. The Largest Laplacian and signless H-eigenvalues of a uniform hypergraph. Linear Algebra and Applications 2015; 469: 1-27
  8. Hu S, Li G, Qi L. A tensor analogy of Yuan’s theorem of the alternative and polynomial optimization with sign structure. Journal of Optimization Theory and Applications 2016; 168: 446-474
  9. Hu S, Li G, Qi L, Song Y. Finding the maximum eigenvalue of essentially nonnegative symmetric tensors via sum of squares programming. Journal of Optimization Theory and Applications 2013; 158: 17-738
  10. Hu S, Huang Z, Ling C, Qi L. On determinants and eigenvalue theory of tensors. Journal of Symbolic Computation 2013; 50: 508-531
  11. Kannike K. Vacuum stability of a general scalar potential of a few fields. European Physical Journal C 2016; 76: 324. doi: 10.1140/epjc/s10052-016-4160-3 [13] Kwon EG, Bae JE. On a generalized Holder inequality. Journal of Inequalities and Applications 2015;88. doi: 10.1186/s13660-015-0612-9 [14] Lim LH. Singular values and eigenvalues of tensors: A variational approach. Computational advances in multi-sensor adaptive processing, 1st IEEE International workshop, IEEE, Piscataway, NJ, 2005; 129-132
  12. Lim LH, Ng MK, Qi L. The spectral theory of tensors and its applications. Numerical Linear Algebra and Applications 2013; 20: 889-890
  13. Liu Y, Zhou G, Ibrahim NF. An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor. Journal of Computational and Applied Mathematics 2010; 235: 286-292
  14. Luo Z, Qi L, Ye Y. Linear operators and positive semidefiniteness of symmetric tensor space