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On the Perron Root of Irreducible Matrices

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Fundamentals of Resource Allocation in Wireless Networks

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 3))

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].

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Authors and Affiliations

  1. Technische Universität Berlin Heinrich Hertz Chair for Mobile Communications and Fraunhofer German-Sino Lab for Mobile Communications, Einsteinufer 37, 10587 Berlin, Germany

    PD Dr.-Ing. habil Sławomir Stańczak & Dr.-Ing Marcin Wiczanowski

  2. Technische Universität Berlin Heinrich Hertz Chair for Mobile Communications and Fraunhofer German-Sino Lab for Mobile Communications and Fraunhofer Institute for Telecommunications Heinrich Hertz Institute, Einsteinufer 37, 10587 Berlin, Germany

    Prof. Dr.-Ing. Dr.rer.nat Holger Boche

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  1. PD Dr.-Ing. habil Sławomir Stańczak
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  2. Dr.-Ing Marcin Wiczanowski
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  3. Prof. Dr.-Ing. Dr.rer.nat Holger Boche
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Correspondence to Sławomir Stańczak .

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© 2009 Springer-Verlag Berlin Heidelberg

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Stańczak, S., Wiczanowski, M., Boche, H. (2009). On the Perron Root of Irreducible Matrices. In: Fundamentals of Resource Allocation in Wireless Networks. Foundations in Signal Processing, Communications and Networking, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79386-1_1

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  • DOI: https://doi.org/10.1007/978-3-540-79386-1_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79385-4

  • Online ISBN: 978-3-540-79386-1

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