Necessary solvability conditions of systems of linear extremal equations

AbstractSystems of linear equations of the form A⊗X = B⊗X and of the form A⊗X = A⊗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 non-trivial solution