%0 Journal Article
%T A Note on the Proof of the Perron-Frobenius Theorem
%A Yun Cheng
%A Timothy Carson
%A Mohamed B. M. Elgindi
%J Applied Mathematics
%P 1697-1701
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.311235
%X This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique for approximating the Perron¡¯s eigenpair of a given positive matrix. We apply the techniques introduced in the paper to approximate the Perron¡¯s interval eigenvalue of a given positive interval matrix.
%K Perron Eigenpair
%K Homotopy
%K Eigencurves
%K Positive Matrices
%K Interval Matrices
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24520