论文标题
通过Bezoutiant对对称性的注释
Notes on symmetrization by Bezoutiant
论文作者
论文摘要
令$ p $为一元双曲线多项式，让$ h $为$ p $和$ p'$的bezoutian矩阵。然后，$ h $对与$ p $相关的Sylvester矩阵对称。 E.Jannelli观察到了这一事实。我们简单地证明了这一事实，同时表明，$ p $ Nuij近似的Bezoutian矩阵家族提供了S.Spagnolo引入的准 - 符合器。将$ h $与对称器连接的关系被J.Leray用于严格双曲线多项式。
Let $p$ be a monic hyperbolic polynomial and let $H$ be the Bezoutian matrix of $p$ and $p'$. Then $H$ symmetrizes the Sylvester matrix associated with $p$. This fact is observed by E.Jannelli. We give a simple proof of this fact and at the same time show that the family of Bezoutian matrices of Nuij approximation of $p$ gives quasi-symmetrizers introduced by S.Spagnolo. A relation connecting $H$with the symmetrizer which was used by J.Leray for strictly hyperbolic polynomial is given.
