Solving an eigenvalve-eigenvector problem in minimax algebra

The purpose of this paper is to solve an example of an eigenvalue eigenvector problem which is formulated in Minimax Algebra. This example is motivated by the Industrial Machine example which is explained in detail in Chapter 1. Also in Chapter 1 we list the basic definition of the binary operations. Next we give the standard axioms on which Minimax Algebra is based.

In Chapter 2, we give some of the theoretical results that arise in Minimax Algebra. Also, the underlying algebraic structures in which the eigenproblem may be viewed is given. A summary of these structures is given in Definition 2.2.

Next, in Chapter 3, we give the related theorems, lemmas, propositions, and corollaries that are needed to establish the procedure for calculating an eigenproblem. These statements make use of the ideas given in Chapter 2, along with some ideas from, graph theory.

Finally, in Chapter 4, we state a particular eigenproblem and solve it using procedures that are established in the previous chapters.