Complexity of matrix problems

Genrich R. Belitskii, Vladimir V. Sergeichuk

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


In representation theory, the classification problem is called wild if it contains the problem of classifying pairs of matrices up to simultaneous similarity. We show in an explicit form that the last problem contains all classification matrix problems given by quivers or posets. Then we prove that this problem does not contain (but is contained in) the problem of classifying three-valent tensors. Hence, every wild classification problem given by a quiver or poset has the same complexity; moreover, a solution of one of them implies a solution of each of the remaining problems. The problem of classifying three-valent tensors is more complicated.

Original languageEnglish
Pages (from-to)203-222
Number of pages20
JournalLinear Algebra and Its Applications
StatePublished - 1 Mar 2003


  • Canonical matrices
  • Classification
  • Representations of quivers and posets
  • Tame and wild matrix problems
  • Tensors

ASJC Scopus subject areas

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


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