ALJABAR MAX PLUS : SUATU KAJIAN TEORI DAN APLIKASI FUNDAMENTALNYA

Abstract

In max-plus algebra we work with the algebra structures consisting of the set

ℝ = ℝ ∪ {−∞} together with operations ab = max(a,b) and ab = a+ b. The additive and multiplicative identities are taken to be  = −∞ and e = 0 respectively. Its operations are associative, commutative and distributive similar to those in conventional algebra.

In this article matrix over max-plus algebra (or in ℝ ) is defined. This article emphasizes on max-plus linear algebra specifically. It is evident that some of the concepts of conventional linear algebra are also possessed by a max-plus version. The solvability of linear systems, such as Ax = b is specifically elaborated in this article.