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Various Proofs of Sylvester's (Determinant) Identity IMACS Symposium SC1993

Summary: Various Proofs of Sylvester's (Determinant) Identity
IMACS Symposium SC­1993
Alkiviadis G. Akritas
, Evgenia K. Akritas,
University of Kansas
Department of Computer Science
Lawrence, KS 66045-2192, USA
Genadii I. Malaschonok
Kiev University
Department of Cybernetics
Vladimirska 64
U-252017 Kiev, Ukraine
current e-mail addresses: akritas@uth.gr and malaschonok@math-iu.tstu.ru
Abstract: Despite the fact that the importance of Sylvester's determinant identity has been
recognized in the past, we were able to find only one proof of it in English [3], with reference to
some others. (Recall that Sylvester stated this theorem without proof [10].) Having used this
identity, recently, in the validity proof of our new, improved, matrix-triangularization subresul-
tant polynomial remainder sequence method [1], we decided to collect all the proofs we found of
this identity -- one in English, four in German and two in Russian, in that order -- in a single
paper [2]. It turns out that the proof in English is identical to an earlier one in German. Due to


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences