Linear Operators That Preserve Arctic Ranks of Boolean Matrices

Abstract

We study some properties of arctic rank of Boolean matrices. We compare the arctic rank with Boolean rank and term rank of a given Boolean matrix. Furthermore, we obtain some characterizations of linear operators that preserve arctic rank on Boolean matrix space.

Keywords

• decomposition of a Boolean matrix
• arctic rank
• term rank
• linear operator
• (<i>P</i>,<i>Q</i>)-operator