Volume 36 • Number 1 • 2013   • Linear Preservers of Extremes of Matrix Pairs Over Nonbinary Boolean Algebra Seok-Zun Song and Mun-Hwan Kang Abstract. The $m\times n$ Boolean matrix $A$ is said to be of Boolean rank $r$ if there exist $m\times r$ Boolean matrix $B$ and $r\times m$ Boolean matrix $C$ such that $A = BC$ and $r$ is the smallest positive integer that such a factorization exists. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebras. 2010 Mathematics Subject Classification: 15A86, 15A03, 15B34 Full text: PDF