Term rank preservers of Boolean matrices

Abstract

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.

Keywords:

• Boolean matrix
• term rank
• Boolean linear operator
• dominate

AMS Subject Classifications::

• 15A04
• 15A09
• 15A86

Acknowledgements

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (No. 2011-0006095).