Geodesic
Linear operators that preserve Boolean rank of Boolean matrices
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 435-440.

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The Boolean rank of a nonzero $m\times n$ Boolean matrix $A$ is the minimum number $k$ such that there exist an $m\times k$ Boolean matrix $B$ and a $k\times n$ Boolean matrix $C$ such that $A=BC$. In the previous research L. B. Beasley and N. J. Pullman obtained that a linear operator preserves Boolean rank if and only if it preserves Boolean ranks $1$ and $2$. In this paper we extend this characterizations of linear operators that preserve the Boolean ranks of Boolean matrices. That is, we obtain that a linear operator preserves Boolean rank if and only if it preserves Boolean ranks $1$ and $k$ for some $1$.
DOI : 10.1007/s10587-013-0027-z
Classification : 15A04, 15A86, 15B34
Keywords: Boolean matrix; Boolean rank; Boolean linear operator 
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Beasley, LeRoy B.; Song, Seok-Zun. Linear operators that preserve Boolean rank of Boolean matrices. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 435-440. doi : 10.1007/s10587-013-0027-z. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0027-z/

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