Geodesic
Linear operators preserving maximal column ranks of nonbinary boolean matrices
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 255-265

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The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
Keywords: Boolean matrix, semiring, linear operator on matrices, congruence operator on matrices, maximal column rank of a matrix, Boolean rank of a matrix 
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Song, Seok-Zun; Yang, Sung-Dae; Hong, Sung-Min; Jun, Young-Bae; Kim, Seon-Jeong. Linear operators preserving maximal column ranks of nonbinary boolean matrices. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 255-265. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_2_a8/