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    A Cycle-Based Bound for Subdominant Eigenvalues of Stochastic Matrices


    Kirkland, Steve (2009) A Cycle-Based Bound for Subdominant Eigenvalues of Stochastic Matrices. Linear and Multilinear Algebra, 57. pp. 247-266. ISSN 0308-1087

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    Abstract

    Given a primitive stochastic matrix, we provide an upper bound on the moduli of its non-Perron eigenvalues. The bound is given in terms of the weights of the cycles in the directed graph associated with the matrix. The bound is attainable in general, and we characterize a special case of equality when the stochastic matrix has a positive row. Applications to Leslie matrices and to Google-type matrices are also considered

    Item Type: Article
    Keywords: subdominant eigenvalue; stochastic matrix; directed graph;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 2191
    Depositing User: Professor Steve Kirkland
    Date Deposited: 14 Oct 2010 14:33
    Journal or Publication Title: Linear and Multilinear Algebra
    Publisher: Taylor & Francis
    Refereed: Yes
    URI:
      Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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