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 , which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to ; 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 matrix has 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}
}
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16 pages