Linear operators that preserve perimeters of Boolean matrices
Bull. Korean Math. Soc. 2008 Vol. 45, No. 2, 355-363
Printed June 1, 2008
Seok-Zun Song, Kyung-Tae Kang, and Hang Kyun Shin
Cheju university, Cheju university, University of seoul education
Abstract : For a Boolean rank $1$ matrix $A = {\bf ab}^t ,$ we define the perimeter of $A$ as the number of nonzero entries in both $\bf a$ and $\bf b$. The perimeter of an $m \times n$ Boolean matrix $A$ is the minimum of the perimeters of the rank-1 decompositions of $A$. In this article we characterize the linear operators that preserve the perimeters of Boolean matrices.
Keywords : Boolean linear operator, perimeter, (U,V)-operator, term rank
MSC numbers : 15A03, 15A04
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