Linear preservers of rank permutability

Anna A. Alieva, Alexander E. Guterman

Research output: Contribution to journalArticlepeer-review


Let F be an arbitrary field and k≥2 be an arbitrary fixed integer. A k-tuple of matrices A1,...,Ak ∈ Mn(F) is called rank permutable if rk(A1A2⋯A k)=rk(Aσ(1)Aσ(2)⋯A σ(k)) for all σ ∈ Sk, where Sk is a symmetric group on k elements. We investigate the set of linear operators on Mn(F) that preserve the set of rank permutable matrix k-tuples.

Original languageEnglish
Pages (from-to)97-108
Number of pages12
JournalLinear Algebra and Its Applications
Issue number1-3 SUPPL.
StatePublished - 1 Jun 2004
Externally publishedYes

Bibliographical note

Funding Information:
This work is partially supported by the grants INTAS 03-55-1919 and MK-1265.2003.01. ∗ Corresponding author. E-mail addresses: (A.A. Alieva), (A.E. Guterman).


  • Linear preservers
  • Matrix relations
  • Rank-permutable matrices


Dive into the research topics of 'Linear preservers of rank permutability'. Together they form a unique fingerprint.

Cite this