双线性函数生成多项式基下的Sylvester型结式矩阵

摘要

构造一类由双线性函数生成的特殊多项式基下的Sylvester型结式矩阵,研究在该基下的Sylvester型结式矩阵与广义Bezout矩阵之间的相互联系.研究得出,诸多性质仍然保持着标准幂基下两类矩阵之间相互关系的类似形式,它们可以看作是标准幂基下两类矩阵关系的延伸.%The author constructed a class of Sylvester-type resultant matrix for the special polynomial basis generated by a bilinear transformation function,and discussed mainly the connections between the Sylvester-type resultant matrix and generalized Bezoutian under such basis.It turned out that these new properties of their connections also kept the similar forms as the ones for the standard power basis and they could be viewed as the extension of classic results on their connections.