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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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

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