Linear maps preserving rank of tensor products of matrices

Abstract

Let be the algebra of all complex matrices. We characterize linear maps satisfyingfor all , .

Keywords:

• linear preserver
• tensor product
• rank of a matrix

AMS Subject Classifications:

• 15A03
• 15A69
• 15A86

Acknowledgements

The authors wish to thank Prof. Chi-Kwong Li and Nung-Sing Sze for their introducing and guiding the topic.

Notes

Jinli Xu was supported by the National Natural Science Foundation Grants of China [grant number 11171294] and the Natural Science Foundation of Heilongjiang Province of China [grant number A201013]. This research was done when Ajda Fošner and Jinli Xu were attending the Summer Research Workshop on Quantum Information Science 2013 at Taiyuan University of Technology. They gratefully acknowledged the support and kind hospitality from the host university.