Graves-Morris, P.R. and Baker, George A. and Woodcock, Chris F.
(1994)
*Cayley's theorem and its application in the theory of vector Pade approximants.*
In: 6th International Congress on Computational and Applied Mathematics, JUL 26-30, 1994, Louvain, Belgium.
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Official URL http://dx.doi.org/10.1016/0377-0427(95)00176-X |

## Abstract

Let A be a matrix of even dimension which is anti-symmetric after deletion of its rth row and column and let R, C be the anti-symmetric matrices formed by modifying the rth row and column of A, respectively. In this case, Cayley's (1857) theorem states that det A = Pf R . Pf C, where Pf R denotes the Pfaffian of R. A consequence of this theorem is an explicit factorisation of the standard determinantal representation of the denominator polynomial of a vector Pade approximant. We give a succinct, modern proof of Cayley's theorem. Then we prove a novel vector inequality arising from investigation of one such Pfaffian, and conjecture that all such Pfaffians are nonnegative.

Item Type: | Conference or workshop item (Paper) |
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Additional information: | 6th International Congress on Computational and Applied Mathematics LOUVAIN, BELGIUM, JUL 26-30, 1994 Belgian Natl Sci Fdn; IBM, Belgium; BBL Antwerpen; SAS Inst; Avia Belgomazout; United Airlines |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | R.F. Xu |

Date Deposited: | 04 Jun 2009 22:24 |

Last Modified: | 29 Apr 2014 15:10 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/19213 (The current URI for this page, for reference purposes) |

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