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.
Original language | English |
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Pages (from-to) | 3912-3927 |
Number of pages | 16 |
Journal | Communications in Algebra |
Volume | 37 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2009 |
Externally published | Yes |
Keywords
- Extended tropical semiring
- Linear algebra
- Linear dependence
- Matrix algebra
- Pseudo invertibility
- Rank of matrices