Various proofs of Sylvester's (determinant) identity
Various proofs of Sylvester's (determinant) identity
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DOI：
10.1016/s0378-4754(96)00035-3
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发表时间：
1996-11-01
影响因子：
4.6
通讯作者：
Malaschonok, GI
中科院分区：
文献类型：
--
作者：
Akritas, AG;Akritas, EK;Malaschonok, GI
尽管西尔维斯特的决定性身份的重要性在过去已经被认识到了，但我们只能在英语中找到一个证据(Bareiss，1968)，参考其他一些证据。(回想一下，西尔维斯特(1857)在没有证明的情况下陈述了这个定理。)最近，在我们新的改进的矩阵三角化次结果多项式余项式序列方法(Akritas等人，1995)的有效性证明中使用了这个恒等式，我们决定将我们找到的关于这个恒等式的所有证明--一个是英语的，四个是德语的，两个是俄语的，顺序是--收集在一篇论文中(Akritas等人，1992)。事实证明，英文的证明与之前的德文的证明是一样的。由于篇幅所限，省略了两个证明。
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 (Bareiss, 1968), with reference to some others. (Recall that Sylvester (1857) stated this theorem without proof.) Having used this identity, recently, in the validity proof of our new, improved, matrix-triangularization subresultant polynomial remainder sequence method (Akritas et al., 1995), 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 (Akritas et al., 1992). It turns out that the proof in English is identical to an earlier one in German. Due to space limitations two proofs are omitted.