On the perron root of irreducible matrices

Abstract

This chapter deals with the Perron root of nonnegative irreducible matrices. Applications abound with nonnegative and positive matrices so that it is natural to investigate their properties. In doing so, one of the central problems is to what extent the nonnegativity (positivity) is inherited by the eigenvalues and eigenvectors. The principal tools for the analysis of spectral properties of irreducible matrices are provided by Perron–Frobenius theory. A comprehensive reference on nonnegative matrices is [4]. Some basic results are summarized in App. A.4. For more information about the Perron–Frobenius theory, the reader is also referred to [5, 6, 7].