Linear systems in (max, +) algebra

Abstract

The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This construction results in the linear closure of the (max, +) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>