Numerical ranges of tensors

Rihuan Ke, Wen Li, Kwok Po NG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general.

Original languageEnglish
Pages (from-to)100-132
Number of pages33
JournalLinear Algebra and Its Applications
Publication statusPublished - 1 Nov 2016

Scopus Subject Areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Approximation
  • Convexity
  • Eigenvalues
  • Numerical range
  • Tensors


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