### Abstract

Spectral properties of the set of all symmetric matrices whose graph is a given tree T are further studied. A new technique based on Smith Normal Form and Hamming Distance is introduced and used to characterize such matrices that have at most four distinct eigenvalues and such matrices that have at most two multiple eigenvalues and whose sum of multiplicities is the maximum possible.

Original language | English (US) |
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Pages (from-to) | 4075-4089 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 438 |

Issue number | 10 |

DOIs | |

State | Published - May 15 2013 |

Externally published | Yes |

### Keywords

- Acyclic matrix
- Diameter
- Hamming distance
- Maximum multiplicity
- Smith normal form

### ASJC Scopus subject areas

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

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## Cite this

Nair, R., & Shader, B. L. (2013). Acyclic matrices with a small number of distinct eigenvalues.

*Linear Algebra and Its Applications*,*438*(10), 4075-4089. https://doi.org/10.1016/j.laa.2012.08.029