Linear rank preservers of tensor products of rank one matrices

Zejun Huang, Shiyu Shi, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

Let n1,…,nkbe integers larger than or equal to 2. We characterize linear maps ϕ:Mn1⋯nk→Mn1⋯nksuch thatrank(ϕ(A1⊗⋯⊗Ak))=1wheneverrank(A1⊗⋯⊗Ak)=1 for all Ai∈Mni,i=1,…,k. Applying this result, we extend two recent results on linear maps that preserve the rank of special classes of matrices.
Original languageEnglish
Pages (from-to)255-271
Number of pages17
JournalLinear Algebra and Its Applications
Volume508
DOIs
Publication statusPublished - 1 Nov 2016

Keywords

  • Linear preserver
  • Partial transpose
  • Rank
  • Realignment
  • Tensor product

ASJC Scopus subject areas

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

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