English

Supertropical Matrix Algebra II: Solving tropical equations

Commutative Algebra 2009-12-07 v3 Combinatorics

Abstract

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of AA, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to AA; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer's rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an n×nn\times n matrix has nn distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.

Keywords

Cite

@article{arxiv.0902.2159,
  title  = {Supertropical Matrix Algebra II: Solving tropical equations},
  author = {Zur Izhakian and Louis Rowen},
  journal= {arXiv preprint arXiv:0902.2159},
  year   = {2009}
}

Comments

16 pages

R2 v1 2026-06-21T12:10:55.029Z