# On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application.

Journal article

Larcombe, Peter J. and Fennessey, Eric J. 2017. On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application.

*Bulletin of the Institute of Combinatorics and its Applications (ICA).*Authors | Larcombe, Peter J. and Fennessey, Eric J. |
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Abstract | Closed form entries for an exponentiated (and arbitrary) 2 ⇥ 2 matrix are established here, and expressed in terms of a specialized Horadam sequence; two proofs of the result are given accordingly, along with examples and observations derived therefrom. The result o↵ers a new formulation of a general class of polynomial families associated with sequences whose ordinary generating functions are governed by quadratic equations. |

Keywords | Sequences; Matrices; Horadam sequence |

Year | 2017 |

Journal | Bulletin of the Institute of Combinatorics and its Applications (ICA) |

Publisher | The Institute of Combinatorics and its Applications |

ISSN | 11831278 |

Web address (URL) | http://hdl.handle.net/10545/622398 |

hdl:10545/622398 | |

Publication dates | Jan 2017 |

Publication process dates | |

Deposited | 21 Mar 2018, 10:26 |

Contributors | University of Derby |

File | File Access Level Open |

File | File Access Level Open |

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https://repository.derby.ac.uk/item/92746/on-sequence-based-closed-form-entries-for-an-exponentiated-general-2-times-2-matrix-a-re-formulation-and-an-application

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