Linear rank preservers of tensor products of rank one matrices

Zejun Huang; Shiyu Shi; Nung Sing Sze

doi:10.1016/j.laa.2016.07.024

Linear rank preservers of tensor products of rank one matrices

Zejun Huang, Shiyu Shi, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

6 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 language	English
Pages (from-to)	255-271
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	508
DOIs	https://doi.org/10.1016/j.laa.2016.07.024
Publication status	Published - 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

More information

10.1016/j.laa.2016.07.024

http://hdl.handle.net/10397/98659

Cite this

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AU - Shi, Shiyu

AU - Sze, Nung Sing

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N2 - 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.

AB - 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.

KW - Linear preserver

KW - Partial transpose

KW - Rank

KW - Realignment

KW - Tensor product

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DO - 10.1016/j.laa.2016.07.024

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VL - 508

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EP - 271

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Linear rank preservers of tensor products of rank one matrices

Abstract

Keywords

ASJC Scopus subject areas

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