Hankel矩阵的性质及其应用

Properties and application of Hankel matrix

利用Bez(a,b)矩阵与其中多项式a(λ)的第一友阵适于的缠绕关系,以及a(λ)和b(λ)的变量变换关系给出了Hankel矩阵所满足的几种新型合同关系、缠绕关系;利用Bezout矩阵的Barnett分解以及Bez(a,b)中a(λ)的零点与其第一友阵特征值的一致性,给出了利用Hankel矩阵的非奇异性判定多项式对互素的新方法.

Some new congruence and twining relations are investigated by using the known one of Bez （ a, b ） with the first companion matrix of a （λ）. A new method to judge the relatively prime on double polynomials a （λ） and b （λ） is given in terms of the Barnett factorition of Bezout matrix and the unanimity of the zeropoints with the eigenvalues of the first companion matrix of a （λ）.