Necessary solvability conditions of systems of linear extremal equations

@article{Butkovic1985NecessarySC,
title={Necessary solvability conditions of systems of linear extremal equations},
author={Peter Butkovic},
journal={Discrete Applied Mathematics},
year={1985},
volume={10},
pages={19-26}
}

Systems of linear equations of the form A®X=B®X and of the form AQX=B® Y over the structure based on linearly ordered commutative group (G, ®, -<) where the role of ® plays the maximum are treated. Necessary solvability conditions are derived using known results concerning eigenvectors of matrices in such structures. In the special case of idempotent, increasing matrices A and B a condition is given which is necessary and sufficient for the existence of a nontrivial solution.