Pseudospectra localizations for generalized tensor eigenvalues to seek more positive definite tensors

  • Chaoqian Li
  • Qilong LiuEmail author
  • Yimin Wei


In this paper, we present the pseudospectrum for generalized tensor eigenvalues, and a set to locate this pseudospectrum. By the relations between H-eigenvalues (Z-eigenvalues) of tensors and generalized tensor eigenvalues, a pseudospectral localization for H-eigenvalues (Z-eigenvalues, respectively) is given to seek positive definite tensors surrounding a positive definite tensor.


Pseudospectral localization Generalized tensor eigenvalues H-eigenvalues Z-eigenvalues Positive definiteness 

Mathematics Subject Classification

15A18 15A69 65F15 65F10 



We would like to thank Dr. Maolin Che and Dr. Xuezhong Wang for their useful discussions on this topic. Chaoqian Li is supported partly by the Shanghai Key Laboratory of Contemporary Applied Mathematics under Grant KBH1411209; the National Natural Science Foundation of China under Grant 11601473; the Applied Basic Research Programs of Science and Technology Department of Yunnan Province under Grant 2018FB001; Program for Excellent Young Talents in Yunnan University; Outstanding Youth Cultivation Project for Yunnan Province under Grant 2018YDJQ021; Yunnan Provincial Ten Thousands Plan Young Top Talents. Qilong Liu is supported by Doctoral Scientific Research Foundation of Guizhou Normal University in 2017 under Grant GZNUD [2017]26. Yimin Wei is supported by the National Natural Science Foundation of China under Grant 11771099 and Innovation Program of Shanghai Municipal Education Commission.


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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsYunnan UniversityYunnanPeople’s Republic of China
  2. 2.School of Mathematical SciencesGuizhou Normal UniversityGuiyangPeople’s Republic of China
  3. 3.School of Mathematics Sciences and Shanghai Key Laboratory of Contemporary Applied MathematicsFudan UniversityShanghaiPeople’s Republic of China

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