Eigenvalues and Eigenvectors of Tropical Matrix

Tropical algebra is an algebraic structure consist of real number and two binary operations i. e maximum or minimum and addition. Matrix with the entries are element of tropical algebra is called tropical matrix. The operations on tropical matrix have the same pattern as the classical matrix, but the operations for the entries of the matrix are tropical algebra operations (maximum or minimum and addition). The terms eigenvalues and eigenvectors of the tropical matrix are slightly different from the classical matrix, so in this study, some basic definitions will be generalize to the tropical algebra. The number of eigenvalues of a matrix in the tropical matrix is similar to the classical matrix i. e n eigenvalues on matrix size nxn. This study shows a method for finding the highest eigenvalues of tropical matrix and corresponding eigenvectors by modifying the existing method.