On tropical matrices of small factor rank |
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Authors: | Yaroslav Shitov |
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Institution: | Moscow State University, Leninskie Gory, 119991, GSP-1, Moscow, Russia |
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Abstract: | The notion of the factor rank of tropical matrices is considered. We construct a linear-time algorithm that either finds a full-rank 3 × 3 submatrix of a given matrix A or concludes that the factor rank of A is less than 3. We show that there exist matrices of factor rank 4 whose 4 × 4 submatrices are all rank deficient. |
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