Congruence of matrix spaces, matrix tuples, and multilinear maps

Genrich R. Belitskii, Vyacheslav Futorny, Mikhail Muzychuk, Vladimir V. Sergeichuk

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These spaces are congruent if R=ST. We prove that if all matrices in V and W are symmetric, or all matrices in V and W are skew-symmetric, then V and W are congruent if and only if they are equivalent. Let F:U×…×U→V and G:U×…×U→V be symmetric or skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U and ψ:V→V that transforms F to G, then there exists such a set with φ1=…=φk.

Original languageEnglish
Pages (from-to)317-331
Number of pages15
JournalLinear Algebra and Its Applications
StatePublished - 15 Jan 2021


  • Congruence
  • Multilinear maps
  • Weak congruence

ASJC Scopus subject areas

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


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