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) (KAR id:19213)
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. | |
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 |
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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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | R.F. Xu |
Date Deposited: | 04 Jun 2009 22:24 UTC |
Last Modified: | 16 Nov 2021 09:57 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/19213 (The current URI for this page, for reference purposes) |
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