Linear rank one preservers on tensor products of Hermitian matrices. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Lau, Jinting; Lim, Ming Huat
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 4(2016)
• Page Start: 717
• Page End: 726
• Publication Date: 2016-04-02
• Subjects: linear preserver -- tensor product -- Hermitian matrix -- rank -- quantum information science; 15A86 -- 15A69 -- 15B57 -- 15A03; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1115811
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this note, we characterize linear maps between spaces of Hermitian matrices over a field with involution which preserve the rank of the identity matrix and the rank of tensor products of rank one Hermitian matrices. It is assumed that the fixed field with respect to the field with involution has at least four elements. We also present some applications of our main result to other preserver problems.