An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications

We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system a...     

n阶常系数线性非齐次常微分方程P（D）x=acose^t＋bsine^t的特解

本利用等价方程组，友矩阵与Jordan标准型，研究了n阶常系数线性非齐次常微分方程P（D）x=acose^t bsine^t其中P（D）=D^n a1D^n-1 … an,D=1/dt,a1,a2,…a,a,b为任意实常数，在友矩阵具有n个不同的特征根的条件下，给出了求上述方程的特解的方法，最后给出一个详细的实例。     

矩阵的初等标准形与线性方程组

指出矩阵的初等标准形理论是线性方程组问题的理论基础     

Non-simple links with tunnel number one

We determine all non-simple links which admit an unknotting tunnel, i.e. links which contain an essential annulus or torus in its exterior and have tunnel number one.

     

具有k重零特征根的矩阵的性质

本文对具有 k重零特征根的矩阵的一些性质进行了探讨 ,这些性质主要涉及到矩阵的秩、矩阵的有理标准形和约当标准形等方面     

Unified tame theorem

The well-known tame theorem tells that for a given tame bocs and a positive integer n there exist finitely many minimal bocses, such that any representation of the original bocs of dimension at most n is isomorphic to the image of a representation of some minimal bocses under a certain reduction functor. In the present paper we will give an alternative statement of the tame theorem in terms of matrix problem, by constructing a unified minimal matrix problem whose indecomposable matrices cover all the canoni...     

欧氏环上矩阵的标准形

将线性变换放至环上线性模中来研究 ,并给出了欧氏环上矩阵的标准形 .     

Jordan标准形定理的初等变换证明

本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 .     

Endomorphism rings of simple modules over group rings

If is a finitely generated nilpotent group which is not abelian-by-finite, a field, and a finite dimensional separable division algebra over , then there exists a simple module for the group ring with endomorphism ring . An example is given to show that this cannot be extended to polycyclic groups.

     

Jordan标准型过渡矩阵的一种新算法

本文通过矩阵函数微分的相关知识,给出了 Jordan标准型过渡矩阵的一种新算法.     

从一道习题的推广看矩阵的标准形理论

通过一道简单习题的多重推广,串联起了实对称阵与实反对称阵的正交相似标准形理论.     

A compound matrix algorithm for the computation of the Smith form of a polynomial matrix

In the present paper is presented a numerical method for the exact reduction of a singlevariable polynomial matrix to its Smith form without finding roots and without applying unimodular transformations. Using the notion of compound matrices, the Smith canonical form of a polynomial matrixM(s)^nxn[s] is calculated directly from its definition, requiring only the construction of all thep-compound matricesC _p (M(s)) ofM(s), 1<pn. This technique produces a stable and accurate numerical algorithm working satisfactorily for any polynomial matrix of any degree.     

方阵的开方问题

运用Jordan标准形理论,完整解决了复数方阵、实数方阵能否开平方、开立方的问题.     

一个被遗漏的Hermite标准形的重要性质及应用

为了使Hermite标准形得到更好的应用,给出了左、右单位矩阵的概念,并指出了矩阵的Hermite行(列)标准形与该矩阵的右(左)单位矩阵的关系,且将其灵活地运用到矩阵广义逆及矩阵方程的讨论中去.     

计算Pascal矩阵加数量矩阵之逆的一种新方法(英文)

In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn＋aIn for arbitrary real number a≠1.     

三阶矩阵的平方根

给出3×3矩阵的平方根公式,并通过实例阐明我们的方法,完善了有关文献中的某些结果．     

关于与给定矩阵可交换的矩阵的多项式表示

文[1]得到:若矩阵A的Jordan标准形中没有纯量矩阵的Jordan块,那么AB=BA的充要条件为B可以化为A的n-1次多项式.本文指出这个结论是错误的.在已有相关文献的基础上,得到了与给定矩阵A可交换的矩阵B是A的多项式的十个等价刻划.     

一类条件数为常数的随机辛阵的性质

对A.Bunse-Gerstner和V.Mehrmann使用的一种随机辛阵的性质进行了研究.证明了1)其可以通过正交相似变换化为一种特殊的Schur标准型;2)其条件数为一常数;3)该常数约为2618.     

模的弱消去问题与qu－正则环

本文考虑模的弱消去问题与正则环的Ｓｔａｂｌｅｒａｎｇｅ条件，引进了ｑｕ－正则环的概念，并用它刻划了一类满足弱消去条件的模，刻划了ｑｕ－正则环，指出一切满足比较公理的正则环均为ｑｕ－正则环．文中还考虑这些结果的应用．例如，刻划了满足弱消去律的拟内射模；证明了素的正则右自内射环上的任意非奇异内射右Ｒ－模可以从直和项中弱消去．