A note on linear preservers of certain ranks of tensor products of matrices

2014/08/19 by Ming-Huat Lim, Ming–Huat Lim · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Algebraic structures and combinatorial models

paper · doi:10.1080/03081087.2014.945445

Abstract

In this note, we give a simple proof as well as an extension of a very recent result of B. Zheng, J. Xu and A. Fosner concerning linear maps between vector spaces of complex square matrices that preserve the rank of tensor products of matrices by using a structure theorem of R. Westwick on linear maps between tensor product spaces that preserve non-zero decomposable elements.

Cited by

• Decomposability preserving linear maps between symmetric spaces

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• Linear maps preserving rank of tensor products of matrices
• Linear rank one preservers on tensor products of Hermitian matrices
• Linear mappings on second symmetric product spaces that Preserve rank less than or equal to one
• Linear maps preserving the higher numerical ranges of tensor product of matrices
• Linear maps preserving (p,k) norms of tensor products of matrices