CHARACTERIZATIONS OF THE COLUMN RANK PRESERVERS OF BOOLEAN MATRICES
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LetMn(B) denote the set of all n£n Boolean matrices. For nonzero A 2Mn(B), the column rank of A is the dimension of the col- umn space of A. In [11], Song obtained that a linear operator onMn(B) is a column rank preserver if and only if it preserves column ranks 1, 2 and 3. In this paper we extend this characterization of linear operators that preserve column ranks of Boolean matrices. Consequently, we ob- tain that a linear operator on Mn(B) is a column rank preserver if and only if it preserves column ranks k and k + 1, where 2 ≤ k ≤ n - 1 if and only if it strongly preserves column rank h, where 3 ≤ h ≤ n.
Abstract
LetMn(B) denote the set of all n£n Boolean matrices. For nonzero A 2Mn(B), the column rank of A is the dimension of the col- umn space of A. In [11], Song obtained that a linear operator onMn(B) is a column rank preserver if and only if it preserves column ranks 1, 2 and 3. In this paper we extend this characterization of linear operators that preserve column ranks of Boolean matrices. Consequently, we ob- tain that a linear operator on Mn(B) is a column rank preserver if and only if it preserves column ranks k and k + 1, where 2 ≤ k ≤ n - 1 if and only if it strongly preserves column rank h, where 3 ≤ h ≤ n.
참고문헌 (12)
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