图的特征多项式的若干性质

图的特征多项式有许多性质，本文给出了特征多项式的指数表达式，特征多项式的导数的几个不同表达式以及高阶导数的图论意义。     

关于方阵多项式的特征问题

对方阵及其矩阵多项式,给出了它们特征值、特征向量之间关系的刻画.     

关于矩阵特征多项式的一个性质

大家都知道,如果两个矩阵A和B相似,那么它们有相同的特征多项式。 即:A,B为n阶矩阵,若存在n阶可逆矩阵P,使得P~(-1)AP=B。 那么它们的特征多项式f_A(λ)和f_B(λ)相同:对于等式P~(-1)AP=B进行变形     

“矩阵特征多项式的一种求法”的一个注记

数学通报一九八八年第九期发表了陈兴龙的“矩阵特征多项式的一种求法”一文,该文给出了求矩阵特征多项式的递椎方法,即     

随机矩阵特征多项式的相关函数的多项式表示

利用正交多项式的性质给出了高斯辛系综中酉辛群上的随机矩阵特征多项式的相关函数和矩的简洁的行列式表示,且行列式的元为正交多项式.     

矩阵及其多项式的若干问题研究

利用多项式理论、线性空间理论研究了矩阵及其多项式的一些性质.     

由主子阵和特殊次序缺损特征对构造Jacobi矩阵

In this paper,an inverse eigenvalue problem of constructing a Jacobian matrix from its prescribed specially ordered defective eigenpairs and a principal subma-trix is considered.The necessary and sufficient conditions for the existence and uniqueness of the solution are derived.Two numerical algorithms and two numer-ical examples are given.     

矩阵方幂的特征多项式

给出四种方法,分别根据特征多项式的性质,多项式根与系数之间的关系以及对称多项式的知识,k次本原单位根,特征多项式的伴侣阵,可在矩阵的特征多项式已知的情况下确定其矩阵方幂的特征多项式.     

关于矩阵多项式特征值界的注记

本文讨论矩阵多项式特征值定域问题.首先对Higham和Tisseur[Linear Algebra Appl.,358(2003),5-22]得到的结果给出较详细的比较.然后利用分块矩阵谱半径的估计给出了获取特征值界的一种新办法.利用这种新办法,不但可以简明地得出很多已有的界,且对椭圆及双曲矩阵多项式得出了特征值的新的界.     

The Fifth and Sixth Coefficients of the Characteristic Polynomial of a Graph

It is well known that the coefficients of the characteristic polynomial of a graph G are determined by the elementary subgraphs of G; in particular there are simple expressions for the four higest coefficients. Here we use an enumeration of elementary subgraphs called k-matchings to obtain expressions for the next two coefficients.     

On the Evaluation of Polynomial Coefficients

The evaluation of the coefficients of a polynomial from its zeros is considered. We show that when the evaluation is carried out by the standard algorithm in finite precision arithmetic, the accuracy of the computed coefficients depends on the order in which the zeros are introduced. An ordering that enhances the accuracy for many polynomials is presented.     

Supernomial Coefficients,Polynomial Identities and q-Series

q-Analogues of the coefficients of xa in the expansion of _j=1 ^N (1 + x + + x^j)^Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the q-supernomial coefficients are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson-fermion-type, based on the continued fraction expansion of p/k and involving the q-supernomial coefficients, are proven. These include polynomial analogues of the Andrews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters.     

关于Bernstein多项式的一个特征

本文建立Ｂｅｒｎｓｔｅｉｎ多项式Ｂｎ（ｆ，ｘ）的阶是的一个特征定理。     

On the Coefficients and Zeros of a Polynomial

Letp(z)=1+∑ⁿ_j=1 b_jz^jbe a complex polynomial. Two theorems on the coefficients and zeros ofp(z) are proved in this paper.     

Laguerre and Disk Polynomial Expansions with Nonnegative Coefficients

We establish Wiener type theorems and Paley type theorems for Laguerre polynomial expansions and disk polynomial expansions with nonnegative coefficients.     

Commuting Differential Operators of Rank 2 with Polynomial Coefficients

Self-adjoint commuting differential operators with polynomial coefficients are considered. These operators form a commutative subalgebra of the first Weyl algebra. New examples of commuting differential operators of rank 2 are found.     

The Distribution Solutions of Ordinary Differential Equation with Polynomial Coefficients

Consider the Differential Equation of the form ty⁽ⁿ⁾(t) + my^(n–1)(t) + ty(t) = 0 (1) where m is any integer and n 2 for t (–, ). It is found that the values of m make the solutions of (1) to be classical, that is the solutions in the space C(–, ) of continuous functions, or the Distributions which are the solutions in the space D_R of Distributions whose supports are bounded on the left.AMS Subject Classification (1991) 46F10     

Complex Zeros of Algebraic Polynomial with Non-Zero Mean Random Coefficients

In this paper we obtain a formula for the average density of the distribution of complex zeros of an algebraic polynomial with random coefficients. The coefficients are assumed independent identical normally distributed random variables with mean and variance ². The value of the average density for the case of =0 and ²=1 was obtained previously. Some limits of the distribution of the complex zeros are provided using the presented formula.