Geodesic
Rank and perimeter preserver of rank-1 matrices over max algebra
Discussiones Mathematicae. General Algebra and Applications, Tome 23 (2003) no. 2, pp. 125-137

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For a rank-1 matrix A = a ⊗ b^t over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or T(A) = U ⊗ A^t ⊗ V with some monomial matrices U and V.
Keywords: max algebra, semiring, linear operator, monomial, rank, dominate, perimeter, (U,V)-operator 
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Song, Seok-Zun; Kang, Kyung-Tae. Rank and perimeter preserver of rank-1 matrices over max algebra. Discussiones Mathematicae. General Algebra and Applications, Tome 23 (2003) no. 2, pp. 125-137. http://geodesic.mathdoc.fr/item/DMGAA_2003_23_2_a3/