The perron-frobenius theorem - Some of its applications

The Perron-Frobenius theorem provides a simple characterization of the eigenvectors and eigenvalues of some types of matrices with nonnegative entries. The importance of the theoreom stems from the fact that eigenvalue problems on these types of matrices arise in different fields of science and engineering. Some of the more common applications of the theorem are in considering the steady state behavior of Markov chains, power control in wireless networks, commodity pricing models in economics, population growth models, and Web search engines.