Extreme sets of rank inequalities over Boolean matrices and their preservers
Commun. Korean Math. Soc. 2013 Vol. 28, No. 1, 1-9
https://doi.org/10.4134/CKMS.2013.28.1.1
Printed January 31, 2013
Seok Zun Song, Mun-Hwan Kang, and Young Bae Jun
Jeju National University, Jeju National University, Gyeongsang National University
Abstract : We consider 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 $T(X) = PXP^{T} $ with some permutation matrix $P$.
Keywords : linear operator, Boolean rank inequality, $(P,Q,B)$-operator, nonbinary Boolean algebra
MSC numbers : Primary 15A86, 15A03, 15A04
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