@inbook{86e44a4d184d4fc1bd348b3cbf39c8ef,
title = "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].",
keywords = "Irreducible Matrix, Large Deviation Principle, Nonnegative Matrice, Perron Root, Spectral Radius",
author = "S{\l}awomir Sta{\'n}czak and Marcin Wiczanowski and Holger Boche",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2009.",
year = "2008",
doi = "10.1007/978-3-540-79386-1_1",
language = "English",
series = "Foundations in Signal Processing, Communications and Networking",
publisher = "Springer Science and Business Media B.V.",
pages = "3--60",
booktitle = "Foundations in Signal Processing, Communications and Networking",
}