Alexander E. Guterman

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We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already received attention, we compare them with the ranks defined in terms of signed tropical determinants or arising from a notion of linear independence introduced by Gondran and Minoux.(More)
We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum, two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action(More)
In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be(More)
Idempotent matrices play a significant role while dealing with different questions in matrix theory and its applications. It is easy to see that over a field any idempotent matrix is similar to a diagonal matrix with 0 and 1 on the main diagonal. Over a semiring the situation is quite different. For example, the matrix J of all ones is idempotent over(More)
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