A Class of Commutative Markov Matrices.

Abstract

A class of Markov matrices which arise in a simple model of a defense system has been examined. The model illustrates a Markov chain which is not time-homogeneous but is still amenable to analytic treatment. The matrices are shown to be commutative and the class is shown to be closed under matrix multiplication. The matrices are also shown to be diagonalizable and the eigenvectors have a simple form, namely composed of elements of Pascal's triangle. A description of the defense system model is given and the implications of the mathematical results for this model are discussed.