Notes on matrix inverse over min-plus algebra

One of the semiring structures is the max-plus algebra, a set with entries   equipped with the operation , which represents the maximum value, and the operation , which means addition. Another semiring structure is the min-plus algebra, a set with entries   equipped with the operation , representing the minimum value, and the operation , which means addition. Matrices over min-plus algebras can have inverses determined by certain conditions. The general inverse type can define the inverse of matrices over min-plus algebras. In this paper, we will develop the characteristics of general inverse matrices over min-plus algebras. The research method used is the literature study method sourced from books and journal articles. The main result of this study is that the generalized inverse of the matrix  can be obtained by determining the matrix with entry  which satisfies .