Linear preservers of rank permutability

Anna A. Alieva; Alexander E. Guterman

doi:10.1016/j.laa.2004.01.001

Linear preservers of rank permutability

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	97-108
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	384
Issue number	1-3 SUPPL.
DOIs	https://doi.org/10.1016/j.laa.2004.01.001
State	Published - 1 Jun 2004
Externally published	Yes

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: ali@isa.ru (A.A. Alieva), guterman@mmascience.ru (A.E. Guterman).

Keywords

Linear preservers
Matrix relations
Rank-permutable matrices

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10.1016/j.laa.2004.01.001

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Linear preservers of rank permutability

Abstract

Bibliographical note

Keywords

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