THE IMPORTANCE OF THE PERRON-FROBENIUS THEOREM

MOHAMMAD TAGHI JAHANDIDEH1
College of Mathematics, Isfahan University of Technology, Isfahan 84156–83111, Isfahan, Iran
jahandid@cc.iut.ac.ir

Abstract. The Perron-Frobenius theorem provides a simple characterization of the eigenvectors and eigenvalues of certain types of matrices with nonnegative entries. The importance of the Perron-
Frobenius theorem stems from the fact that eigenvalue problems on these types of matrices frequently arise in many different fields of science and engineering. In this paper, we will examine the statement of the Perron-Frobenius theorem and discuss several examples of its use, such as in graph theory, stochastic matrices, Markov chains, power-control problems, and finding PageRank scores.