### Abstract

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.

Original language | English |
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Pages (from-to) | 175-185 |

Number of pages | 11 |

Journal | Special Matrices |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 3 Aug 2015 |

### Keywords

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

## Cite this

Tudisco, F. (2015). A note on certain ergodicity coefficients.

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