Additive rank-one preservers between spaces of rectangular matrices

Xian Zhang, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

Suppose F is a field and m,n,p,q are positive integers. Let Mmn(F) be the set of all m × n matrices over F, and let Mmn1(F) be its subset consisting of all rank-one matrices. A map φ : Mmn(F) → Mpq(F) is said to be an additive rank-one preserver if φ(Mmn(F)) ⊆ Mpq1(F) and φ(A + B) = φ(A) + φ(5) for any A, B ∈ Mmn(F). This article describes the structure of all additive rank-one preservers from Mmn(F) to Mpq(F).
Original languageEnglish
Pages (from-to)417-425
Number of pages9
JournalLinear and Multilinear Algebra
Volume53
Issue number6
DOIs
Publication statusPublished - 1 Nov 2005
Externally publishedYes

Keywords

  • Additive preserver
  • Field
  • Matrix space
  • Rank one

ASJC Scopus subject areas

  • Algebra and Number Theory

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