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. 

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