An eigenvalue problem for even order tensors with its applications

Lu Bin Cui, Chuan Chen, Wen Li*, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

In this paper, we study an eigenvalue problem for even order tensors. Using the matrix unfolding of even order tensors, we can establish the relationship between a tensor eigenvalue problem and a multilevel matrix eigenvalue problem. By considering a higher order singular value decomposition of a tensor, we show that higher order singular values are the square root of the eigenvalues of the product of the tensor and its conjugate transpose. This result is similar to that in matrix case. Also we study an eigenvalue problem for Toeplitz/circulant tensors, and give the lower and upper bounds of eigenvalues of Toeplitz tensors. An application in image restoration is also discussed.

Original languageEnglish
Pages (from-to)602-621
Number of pages20
JournalLinear and Multilinear Algebra
Volume64
Issue number4
DOIs
Publication statusPublished - 2 Apr 2016

Scopus Subject Areas

  • Algebra and Number Theory

User-Defined Keywords

  • circulant tensors
  • eigenvalues
  • eigenvectors
  • higher order singular value decomposition
  • multilevel matrices
  • tensors
  • Toeplitz tensors

Fingerprint

Dive into the research topics of 'An eigenvalue problem for even order tensors with its applications'. Together they form a unique fingerprint.

Cite this