Rank and perimeter preservers of boolean rank-1 matrices

Seok-Zun Song; LeRoy B. Beasley; Gi-Sang Cheon; Young-Bae Jun

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2004; 41(2): 397-406

Printed March 1, 2004

Rank and perimeter preservers of boolean rank-1 matrices

Seok-Zun Song, LeRoy B. Beasley, Gi-Sang Cheon, and Young-Bae Jun

Cheju National University, Utah State University, Daejin University, Gyeongsang National University

Abstract

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Abstract

For a Boolean rank-$1$ matrix $A= {\bf a \bf b}^t$, we define the $perimeter$ of $A$ as the number of nonzero entries in both $\bf a$ and $\bf b$. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-1 matrices.

Keywords: Boolean linear operator, perimeter, (U,V)-operator

MSC numbers: Primary 15A03, 15A04