### Abstract

Language | English |
---|---|

Pages | 175-185 |

Number of pages | 11 |

Journal | Special Matrices |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 3 Aug 2015 |

### Fingerprint

### Keywords

- ergodicity
- eigenvalues
- matrices
- linear systems
- pagerank
- coefficients

### Cite this

*Special Matrices*,

*3*(1), 175-185. https://doi.org/10.1515/spma-2015-0016

}

*Special Matrices*, vol. 3, no. 1, pp. 175-185. https://doi.org/10.1515/spma-2015-0016

**A note on certain ergodicity coefficients.** / Tudisco, Francesco.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on certain ergodicity coefficients

AU - Tudisco, Francesco

PY - 2015/8/3

Y1 - 2015/8/3

N2 - We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector problem Ax = x as a particular M-matrix linear system, whose coefficient matrix can be defined in terms of the entries of A. Such property turns out to generalize the two known equivalent formulations of the Pagerank centrality of a graph.

AB - We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector problem Ax = x as a particular M-matrix linear system, whose coefficient matrix can be defined in terms of the entries of A. Such property turns out to generalize the two known equivalent formulations of the Pagerank centrality of a graph.

KW - ergodicity

KW - eigenvalues

KW - matrices

KW - linear systems

KW - pagerank

KW - coefficients

U2 - 10.1515/spma-2015-0016

DO - 10.1515/spma-2015-0016

M3 - Article

VL - 3

SP - 175

EP - 185

JO - Special Matrices

T2 - Special Matrices

JF - Special Matrices

SN - 2300-7451

IS - 1

ER -