Example of the Matrix of Size 6×6 with Different Tropical Rank and Kapranov Rank / Shitov Ya.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 5. P. 58-61 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
We present an example of a 6×6 matrix A such that rkt(A) = 4, rkK(A) = 5. This disproves the conjecture formulated by M. Chan, A. Jensen, and E. Rubei.
Key words:
tropical semiring, tropical rank, Kapranov rank, tropical basis.