Abstract
The Boolean matrix A is said to be of Boolean rank r if there exist Boolean matrix B and Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of with some permutation matrix P.
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