Multiplicative structure of 2x2 tropical matrices

Abstract

We study the algebraic structure of the semigroup of all $2\times 2$ tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of Green's relations and the idempotents and maximal subgroups of this semigroup.

21 pages, 5 figures

References in corpus (1)

• Reachability problems for products of matrices in semirings