Tensor logarithmic norm and its applications

Weiyang DING, Zongyuan Hou, Yimin Wei*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

18 Citations (Scopus)


Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi-norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems.

Original languageEnglish
Pages (from-to)989-1006
Number of pages18
JournalNumerical Linear Algebra with Applications
Issue number6
Publication statusPublished - 1 Dec 2016

Scopus Subject Areas

  • Algebra and Number Theory
  • Applied Mathematics

User-Defined Keywords

  • logarithmic norm
  • spectral abscissa
  • stability of dynamical systems
  • tensor eigenvalue
  • tensor norm
  • tensor pair


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