The Tropical Rank of a Tropical Matrix
نویسنده
چکیده
In this paper we further develop the theory of matrices over the extended tropical semiring. Introducing a notion of tropical linear dependence allows for a natural definition of matrix rank in a sense that coincides with the notions of tropical regularity and invertibility.
منابع مشابه
On tropical and Kapranov ranks of tropical matrices
Let M be a tropical matrix (k + x) × (k + x ′) for some k, x , x ′ ∈ N − {0} with tropical rank k. We show that Kapranov rank is k too if x and x ′ are not too big; namely if we are in one of the following cases: a) k ≥ 6 and x , x ′ ≤ 2 b) k = 4, 5, x ≤ 2 and x ′ ≤ 3 (or obviuosly the converse, that is x ≤ 3 and x ′ ≤ 2) c) k = 3 and either x , x ′ ≤ 3 or x ≤ 2 and x ′ ≤ 4 (or obviuosly the co...
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