LINEAR OPERATORS THAT PRESERVE PERIMETERS OF MATRICES OVER SEMIRINGS Song, Seok-Zun; Kang, Kyung-Tae; Beasley, Leroy B.;
A rank one matrix can be factored as for vectors and of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in plus the number of nonzero entries in . A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.
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