Eigenvalue, Eigenvector, Eigenmode of Reducible Matrix and Its Application

There are three essential components of matrix that must be understood in the process of completing the scheduling problems using max-plus algebra. They are eigenvalue, eigenvector, and eigenmode. The result showed that the reducible matrix does not necessarily have eigenvalue. If it has eigenvalue, the eigenvalue is not necessarily unique with finite value. The eigenvector corresponding to the eigenvalue of reducible matrix is not unique that contains at least a finite element. Furthermore, the eigenmode of a regular reducible matrix is not unique with all finite elements for each component.