Rank preserver of Boolean matrices

Seok-Zun Song; Kyung-Tae Kang; Young-Bae Jun

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Bull. Korean Math. Soc. 2005; 42(3): 501-507

Printed September 1, 2005

Rank preserver of Boolean matrices

Seok-Zun Song, Kyung-Tae Kang, and Young-Bae Jun

Cheju National University, Cheju National University, Gyeongsang National University

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Abstract

A Boolean matrix with rank $1$ is factored as a left factor and a right factor. The perimeter of a rank-$1$ Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

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

MSC numbers: Primary 15A23, 15A04, 15A03