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 
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/
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[1] R.B. Bapat, A max version of the Perron-Frebenius theorem, Linear Algebra Appl. 275-276 (1998), 3-18.

[2] R.B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear and Multilinear Algebra 48 (2000), 149-164.

[3] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77.

[4] L.B. Beasley, S.-Z. Song and S.-G. Lee, Zero term rank preservers, Linear and Multilinear Algebra 48 (2001), 313-318.

[5] S.-Z. Song and S.-R. Park, Maximal column rank preservers of fuzzy matrices, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 207-218.