Determinant of a matrix over min-plus algebra

Abstract

Max-plus algebra is a set ℝ max = ∪ ℝ {ϵ}, with ℝ is the set of all real numbers and e = -∞ equipped with ⊕ (maximum) and ⊗ (plus) operation. Another algebra that can be learned is the min-plus algebra. Min-plus algebra is a set ℝ min = ℝ ∪ {ϵ′}, with ℝ is the set of all real number and ϵ = +∞ equipped with ⊕′ (minimum) and ⊗ (plus) operation. Any square matrices over max-plus algebra can be related to the determinant. The determinant term of max-plus algebra is represented by the permanent and dominant. This study will discuss the determinant of a matrix over min-plus algebra.