Beasley, LeRoy B., and Song, Seok-Zun. "Linear operators that preserve Boolean rank of Boolean matrices." Czechoslovak Mathematical Journal 63.2 (2013): 435-440. <http://eudml.org/doc/260698>.
@article{Beasley2013,
abstract = {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 $1<k\le m$.},
author = {Beasley, LeRoy B., Song, Seok-Zun},
journal = {Czechoslovak Mathematical Journal},
keywords = {Boolean matrix; Boolean rank; Boolean linear operator; Boolean matrix; Boolean rank; Boolean linear operator; preserver},
language = {eng},
number = {2},
pages = {435-440},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear operators that preserve Boolean rank of Boolean matrices},
url = {http://eudml.org/doc/260698},
volume = {63},
year = {2013},
}
TY - JOUR
AU - Beasley, LeRoy B.
AU - Song, Seok-Zun
TI - Linear operators that preserve Boolean rank of Boolean matrices
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 435
EP - 440
AB - 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 $1<k\le m$.
LA - eng
KW - Boolean matrix; Boolean rank; Boolean linear operator; Boolean matrix; Boolean rank; Boolean linear operator; preserver
UR - http://eudml.org/doc/260698
ER -
