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The importance of Perron-Frobenius Theorem in ranking problems

Author

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  • Alberto Peretti

    (Department of Economics (University of Verona))

Abstract

The problem of ranking a set of elements, namely giving a ``rank'' to the elements of the set, may be tackled in many different ways. In particular a mathematically based ranking scheme can be used and sometimes it may be interesting to see how different can be the results of a mathematically based method compared with some more heuristic ways. In this working paper some remarks are presented about the importance, in a mathematical approach to ranking schemes, of a classical result from Linear Algebra, the Perron--Frobenius theorem. To give a motivation of such an importance two different contexts are taken into account, where a ranking problem arises: the example of ranking football/soccer teams and the one of ranking webpages in the approach proposed and implemented by Google's PageRank algorithm.

Suggested Citation

  • Alberto Peretti, 2014. "The importance of Perron-Frobenius Theorem in ranking problems," Working Papers 26/2014, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:26/2014
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    File URL: http://dse.univr.it/home/workingpapers/wp2014n26.pdf
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    References listed on IDEAS

    as
    1. Alberto Peretti & Alberto Roveda, 2014. "On the mathematical background of Google PageRank algorithm," Working Papers 25/2014, University of Verona, Department of Economics.
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    Cited by:

    1. Alberto Peretti, 2017. "A linear model for a ranking problem," Working Papers 20/2017, University of Verona, Department of Economics.
    2. Alberto Peretti, 2016. "The algebraic approach to some ranking problems," Working Papers 22/2016, University of Verona, Department of Economics.

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    1. Alberto Peretti, 2016. "The algebraic approach to some ranking problems," Working Papers 22/2016, University of Verona, Department of Economics.
    2. Alberto Peretti, 2017. "A linear model for a ranking problem," Working Papers 20/2017, University of Verona, Department of Economics.

    More about this item

    Keywords

    Ranking scheme; Linear transformation; Eigenvalue; Dominant eigenvalue;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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