For a rank-1 matrix 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 with some monomial matrices U and V.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1068,
author = {Seok-Zun Song and Kyung-Tae Kang},
title = {Rank and perimeter preserver of rank-1 matrices over max algebra},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {23},
year = {2003},
pages = {125-137},
zbl = {1059.15008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1068}
}
Seok-Zun Song; Kyung-Tae Kang. Rank and perimeter preserver of rank-1 matrices over max algebra. Discussiones Mathematicae - General Algebra and Applications, Tome 23 (2003) pp. 125-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1068/
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