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1·There are two kinds of method to calculate the eigenvalues of a matrix: characteristic polynomial method and QR method.

结合多项式方法和QR方法各自的特点，提出了一种计算矩阵重特征值的方法。

2·In this paper, the concept of the characteristic polynomial, the converse graph, the symmetrical closure and others are defined.

本文引入有向图的特征多项式、反图、对称闭包等概念。初步探讨它们与图的某些整体性质的关系。

3·In this paper, we present an iterative method for determining whether all roots of characteristic polynomial are on the left half-plane.

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。

4·HMO characteristic polynomial and select eigenvalues for many heterocyclic benzenoids are calculated by using chemical graph theory methods.

应用化学图论计算了杂环芳烃HMO的选择本征值和本征多项式。

5·A Characteristic polynomial algorithm for computation of Chebyshev polynomial over finite field is modified to achieve faster execution speed.

对计算有限域上切比雪夫多项式的特征多项式算法进行改进以提高算法的执行速度。

6·This paper introduces the reduced order theory of characteristic polynomial and its application in the higher order matrix aspects are presented.

研究特征多项式的降阶定理以及它在高阶矩阵方面的应用。

7·The property of companion matrix is studied, and the method of calculating the characteristic polynomial of matrix with similar transformation is explained.

研究了友阵的性质，论述了用相似变换计算矩阵特征多项式的方法。

8·Since this simplified algorithm requires no computation of the characteristic polynomial of the controlled system, it makes the practical calculation convenient.

该算法不需要计算控制系统的特征多项式，因此给实际计算带来方便。

9·The formulae for the number of loops, edges, triangles, pairs of two-way nodes and pairs of one-way nodes are deduced by the coefficients of a characteristic polynomial, so on.

推导出由特征多项式的系数表示的线图（无重边图）中圈的个数，双向结点对个数，单向结点对个数及简单图中有向三角形个数的计算公式，等等。

10·Least square method of polynomial or the method based on the given function are used to fit pump characteristic curve in pump selection or operation.

在水泵的选型或运行中，通常采用多项式的最小二乘法或根据假设的函数关系来拟合水泵性能曲线。