The Tropical Rank of a Tropical Matrix

By Zur Izhakian, Louis H. Rowen. 2006

91 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a541e7e39f41dddbb2b93403879b905c9b324302

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Marianne Akian
2. Alexander E. Guterman
3. Stephane Gaubert
4. Louis H. Rowen
5. Zur Izhakian
6. Manfred Knebusch

In Computational Mathematics

1. Stephane Gaubert
2. Marianne Akian
3. Alexander E. Guterman
4. Zur Izhakian
5. Louis H. Rowen

In Computational Theory and Mathematics

1. Marianne Akian
2. Stephane Gaubert
3. Alexander E. Guterman
4. Louis H. Rowen
5. Zur Izhakian
6. Manfred Knebusch
7. Ricardo D. Katz
8. Peter Butkovic

Citations in the corpus

• Linear independence over tropical semirings and beyond (2008, background): “In [Izh08b] the following notion of linear dependence over Te is investigated.”
• Supertropical linear algebra (2010, result): “Explicitly, properties of matrices were studied in [9], [10], [11], and [12], where the main theme is to replace the max-plus algebra by a cover, called the supertropical semiring, which permits one to formulate stronger results which are amenable to proofs more in line with classical matrix theory.”
• Tropical Cramer Determinants Revisited (2013, background): “We obtain existence or uniqueness results, which extend or refine earlier results of Gondran and Minoux (1978), Plus (1990), Gaubert (1992), Richter-Gebert, Sturmfels and Theobald (2005) and Izhakian and Rowen (2009).”