Perimeter preserver of matrices over semifields
Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)
Czechoslovak Mathematical Journal
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For a rank- matrix , we define the perimeter of as the number of nonzero entries in both and . We characterize the linear operators which preserve the rank and perimeter of rank- matrices over semifields. That is, a linear operator preserves the rank and perimeter of rank- matrices over semifields if and only if it has the form , or with some invertible matrices U and V.