这些代数条件表示为由椭圆与抛物线，椭圆与双曲线确定的广义特征多项式的根的分布。
The algebraic condition can be represented by the distribution of the roots of the generalized characteristic equation of the ellipse and parabola (hyperbola).
本文讨论了具有一个零特征根的非线性齐次系统的局部拓扑结构，并给出利用系统右端多项式系数的判断准则。
In this paper, we discuss the locally topological structures of nonlinear homogeneous systems with one zero characteristic root, and give a criteria by the right-hand polynomial coefficients.
本文提出一种确定特征多项式的全部根是否位于左半平面的迭代法。
In this paper, we present an iterative method for determining whether all roots of characteristic polynomial are on the left half-plane.
本文证明了球面有限点集的伪对称性可以完全由其特征多项式的根来刻画，并得到了在度量加运算下伪对称性具有封闭性。
In this paper, we show that the Pseudo-Symmetric property of spherical point set can be characterized by the eigen values of eigenpolynomial and it has the closeness under the metric sum operation.
本文在复数域上证明了哈密尔顿-凯莱定理，并给出方阵A的特征多项式的全部矩阵根。
The paper proved the Hamilton-Cayley theorem in complex number space, and indicated the all matrix root of the sign multinomial of matrix A.
本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。
It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.
考虑阻尼力后，结构的特征方程应有复数根，因而通常用于求解多项式方程实数根的二分法不再适用。
The consideration of damping force leads to a fact that there exist complex roots to the characteristic equation for the structures.
考虑阻尼力后，结构的特征方程应有复数根，因而通常用于求解多项式方程实数根的二分法不再适用。
The consideration of damping force leads to a fact that there exist complex roots to the characteristic equation for the structures.
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