Bijective linear rank preservers for spaces of matrices over antinegative semirings

We classify the bijective linear operators on spaces of matrices over antinegative commutative semirings with no zero divisors which preserve certain rank functions such as the symmetric rank, the factor rank and the tropical rank. We also classify the bijective linear operators on spaces of matrice...

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Bibliographic Details
Published in:Linear algebra and its applications 2011-10, Vol.435 (7), p.1666-1671
Main Author: Pereira, Rajesh
Format: Article
Language:English
Subjects:
Linear preservers
Matrix theory
Rank
Semirings
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Summary:We classify the bijective linear operators on spaces of matrices over antinegative commutative semirings with no zero divisors which preserve certain rank functions such as the symmetric rank, the factor rank and the tropical rank. We also classify the bijective linear operators on spaces of matrices over the max-plus semiring which preserve the Gondran–Minoux row rank or the Gondran–Minoux column rank.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.06.018