Abstract
For a Boolean rank 1 matrix <TEX>$A=ab^t$</TEX>, we define the perimeter of A as the number of nonzero entries in both a and b. The perimeter of an <TEX>$m{\times}n$</TEX> 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.
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