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 |
|---|---|
| Pages (from-to) | 3912-3927 |
| Number of pages | 16 |
| Journal | Communications in Algebra |
| Volume | 37 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 2009 |
Bibliographical note
Funding Information:The first author would like to express his sincere thanks to Prof. E. Shustin for his invaluable help. I am deeply grateful to him for our fertile discussions. The author has been supported by The German–Israeli Foundation for Research and Development by Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.
Funding
The first author would like to express his sincere thanks to Prof. E. Shustin for his invaluable help. I am deeply grateful to him for our fertile discussions. The author has been supported by The German–Israeli Foundation for Research and Development by Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.
| Funders | Funder number |
|---|---|
| Hermann Minkowski Minerva Center for Geometry | |
| German-Israeli Foundation for Scientific Research and Development | |
| Tel Aviv University |
Keywords
- Extended tropical semiring
- Linear algebra
- Linear dependence
- Matrix algebra
- Pseudo invertibility
- Rank of matrices