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The Tropical Rank of a Tropical Matrix |
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| Authors: | Zur Izhakian Louis Rowen |
| Institution: | 1. Department of Mathematics , Bar-Ilan University , Ramat-Gan, Israel;2. CNRS et Universite Denis Diderot , Paris 7, Paris, France zzur@math.biu.ac.il;4. Department of Mathematics , Bar-Ilan University , Ramat-Gan, Israel |
| Abstract: | In this article, we develop further the theory of matrices over the extended tropical semiring. We introduce the notion of tropical linear dependence, enabling us to define matrix rank in a sense that coincides with the notions of tropical nonsingularity and invertibility. |
| Keywords: | Extended tropical semiring Linear algebra Linear dependence Matrix algebra Pseudo invertibility Rank of matrices |