### Abstract

It is shown that every matrix in a large class of n-by-n doubly cyclic Z^{+} matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.

Original language | English (US) |
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Pages (from-to) | 3576-3580 |

Number of pages | 5 |

Journal | Linear Algebra and Its Applications |

Volume | 439 |

Issue number | 11 |

DOIs | |

State | Published - Dec 1 2013 |

### Keywords

- Doubly-cyclic Z matrices
- Eigenvalue location

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Johnson, C. R., Price, Z., & Spitkovsky, I. M. (2013). The distribution of eigenvalues of doubly cyclic Z

^{+}-matrices.*Linear Algebra and Its Applications*,*439*(11), 3576-3580. https://doi.org/10.1016/j.laa.2013.09.021