P. Brockman, T. Carson, Y. Cheng, T. M. Elgindi, K. Jensen, X. Zhoun and M. B. M. Elgindi, “Homotopy Method for the Eigenvalues of Symmetric Tridiagonal Matrices,” Journal of Computational and Applied Mathematics, Vol. 237, No. 1, 2012, pp. 644-653. doi:10.1016/j.cam.2012.08.010

has been cited by the following article:

• TITLE: A Note on the Proof of the Perron-Frobenius Theorem

  AUTHORS: Yun Cheng, Timothy Carson, Mohamed B. M. Elgindi

  KEYWORDS: Perron Eigenpair; Homotopy; Eigencurves; Positive Matrices; Interval Matrices

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 20, 2012

  ABSTRACT: 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.