Maja Ilc (2012) On the rank of a tropical matrix. EngD thesis.
Rank of a real matrix can be defined in many equivalent way. It is interesting that the rank of a matrix over the tropical semiring can vary according to these definitions, which means that the ways in which we can determine rank are no longer equivalent. In the thesis we focus on three rank definitions; rank of a matrix determined by the maximum regular minor, row rank and column rank. We demonstrate with example that with the extension of tropical semiring we can achieve similar results to those over reals.
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