Tropical Linear Algebra: Notions of Rank Over the Tropical Semiring
William D Wise · OhioLink ETD Center (Ohio Library and Information Network) · 2015
Three formulations of the rank of a matrix that are equivalent in classical linear algebra give rise to distinct notions of rank over the tropical semiring.This paper explores these three concepts of tropical rank and their relationships with one another, working up to a proof of the inequality that relates the three.