1. Linear operators that preserve Boolean rank of Boolean matrices
- Creator:
- Beasley, Leroy B. and Song, Seok-Zun
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Boolean matrix, Boolean rank, and Boolean linear operator
- Language:
- English
- Description:
- 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 $1<k\leq m$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public