On tropical supereigenvectors

The task of finding tropical eigenvectors and subeigenvectors, that is non-trivial solutions to A⊗x=λ⊗x and A⊗x≤λ⊗x in the max-plus algebra, has been studied by many authors since the 1960s. In contrast the task of finding supereigenvectors, that is solutions to A⊗x≥λ⊗x, has attracted attention only recently. We present a number of properties of supereigenvectors focusing on a complete characterization of the values of λ associated with supereigenvectors and in particular finite supereigenvectors. The proof of the main statement is constructive and enables us to find a non-trivial subspace of finite supereigenvectors. We also present an overview of key related results on eigenvectors and subeigenvectors.