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Cayley's theorem and its application in the theory of vector Pade approximants

Graves-Morris, P.R., Baker, George A., Woodcock, Chris F. (1994) Cayley's theorem and its application in the theory of vector Pade approximants. Journal of Computational and Applied Mathematics, 66 (1-2). pp. 255-265. ISSN 0377-0427. (doi:10.1016/0377-0427(95)00176-X) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
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: Article
DOI/Identification number: 10.1016/0377-0427(95)00176-X
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
Uncontrolled keywords: Cayley, Clifford, Pfaffian, Vector Padé approximant, Inequality, Skew-symmetric, Anti-symmetric
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: R.F. Xu
Date Deposited: 04 Jun 2009 22:24 UTC
Last Modified: 10 Jun 2019 09:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/19213 (The current URI for this page, for reference purposes)
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