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 AbstractGiven 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 | Keywords: | subdominant eigenvalue; stochastic matrix; directed graph; |
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| Subjects: | Science & Engineering > Hamilton Institute |
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| ID Code: | 2191 |
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| Deposited By: | Professor Steve Kirkland |
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| Deposited On: | 14 Oct 2010 15:33 |
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| Journal or Publication Title: | Linear and Multilinear Algebra |
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| Publisher: | Taylor & Francis |
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| Refereed: | Yes |
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