Graves-Morris, P.R. and Baker, G.A. and Woodcock, C.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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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)|
|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:||12 Jun 2012 09:53|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/19213 (The current URI for this page, for reference purposes)|
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