Characteristic Polynomial of a Triangular and Diagonal Strictly Double ℝ -astic Matrices over Interval Max-Plus Algebra

Max-plus algebra is the set ℝ ε = ℝ ∪ { ε } where ℝ is a set of all real numbers and ε = –∞ which is endowed with max (⊕) and plus (⊗) operations. A matrix in which its components are the element of ℝ ε is called matrix over max-plus algebra. From matrix, we can define characteristic polynomial over max-plus algebra. Max-plus algebra has been generalized into interval max-plus algebra. Interval max-plus algebra is the set of interval over ℝ ε , denoted by I ( ℝ ) ε , which is endowed with ⊕ ¯ and ⊗ ¯ operations. A matrix in which its components are the element of I ( ℝ ) ε is called interval matrix. Interval matrix has some unique forms, two of which are triangular and diagonal strictly double ℝ -astic matrices. From interval matrix, we can define characteristic polynomial over interval max-plus algebra which is used to determine eigenvalues. In this research will discussed about the characteristic polynomial of a triangular and diagonal strictly double ℝ-astic matrices over interval max-plus algebra that will also be used to determine eigenvalues.