Fuzzy标准矩阵及Fuzzy强标准矩阵

本文在格L=[0,1]上定义了Fuzzy标准矩阵及Fuzzy强标准矩阵,得出了他们的一些基本性质。证明了Fuzzy标准矩阵是幂收敛阵;给出了Fuzzy强标准矩阵的判别条件及Fuzzy强标准矩阵是幂等的充要条件。最后对Fuzzy强标准矩阵的秩进行了讨论。     

关于对称R—循环分块矩阵

给出了对称Ｒ－循环分块矩阵的概念，讨论了它的一些性质，当Ｒ＝Ｉｎ时，得到了它的分解定理及标准形。     

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     

具有k重零特征根的矩阵的性质

本对具有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。     

漫谈在各种变换下的矩阵标准形

在矩阵论中,关于标准形的问题占有相当重要的地位,这是因为把矩阵化成标准形后,不仅仅是形式简单,而更重要的是利用标准形解决理论上和实际中的有关问题是十分方便的。笔者根据高等代数的教学实践,把在各种变换下的矩阵标准形进行了概括和综述,这将作为从事高等代数教学同行的引玉之砖。     

层次分析正互反矩阵的Hadamard乘积分析法

定义了标准形 ～ 型 ,并指出任一正互反矩阵可唯一分解为任一种标准形和一个一致性矩阵的Hadamard乘积 .     

标准混合差集矩阵的构造

通过利用差集矩阵和投影矩阵的正交分解之间的关系,首先提出了构造小的标准混合差集矩阵的一般方法.其次,给定一个阶为r+1的标准混合差集矩阵和一个阶为r的差集矩阵,首先提出了构造阶为r(r+1)的标准混合差集矩阵的一般方法.如果阶为r的差集矩阵不存在但一个试验次数为r~2的正交表存在,也可以通过它们构造阶数较大的标准混合差集矩阵.     

关于常系数齐次线性微分方程组的解法研究

利用凯莱-哈密顿定理给出矩阵指数函数eAt的简洁计算方法;同时利用约当标准形推导出求常系数齐次线性微分方程组通解的循环公式.     

三阶矩阵的平方根

本文利用矩阵的特征值和Jordan标准形，给出了三阶矩阵的所有平方根。     

关于合成矩阵的正定性

利用标准形分别给出了复正定矩阵的合成矩阵为复正定矩阵和实正定矩阵的合成矩阵为实正定矩阵的充分必要条件,其结果简单而实用.     

有强法式的体上矩阵

设D为除环,A∈Dn×n,则可用初等变换将λI-A化简为对角阵A= diag(1,…,1,φ1,…,φr),其中(?)i为D上首1多项式并且φ1|…|φr.如果这个对角阵A在形状上是唯一的,则称A是有强法式的矩阵.本文应用中心原子因子与初等因子给出了体上有强法式的矩阵的本质刻画,给出了体上矩阵有强法式的一些充要条件.     

Fast computation of Hermite normal forms of random integer matrices

This paper is about how to compute the Hermite normal form of a random integer matrix in practice. We propose significant improvements to the algorithm by Micciancio and Warinschi, and extend these techniques to the computation of the saturation of a matrix. We describe the fastest implementation for computing Hermite normal form for large matrices with large entries.     

关于矩阵相似中变换矩阵的一般形式

本文利用 Jordan标准形理论 ,给出了矩阵相似中的变换矩阵的一般表达形式 .     

Generalized normal matrices

A matrix A ∈ Mn（C） is called generalized normal provided that there is a positive definite Hermite matrix H such that HAH is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.     

On the computation of the Smith normal form of compound matrices

Compound matrices are encountered in many fields such as Matrix Theory, Systems Theory, Control Theory, etc. In the present paper we develop an efficient algorithm computing the Smith normal form of compound matrices. This algorithm is based on a new theorem establishing an equivalence relation between the Smith normal form of the compounds of a given matrix and the compounds of the Smith normal form of the given matrix. This revised version was published online in June 2006 with corrections to the Cover Date.     

Skew-Hadamard Matrices and the Smith Normal Form

We show that the Smith normal form of every skew-Hadamard matrix of order 4m is diag[1,2,...,2, 2m,...,2m,4m]     

Applications of the duality method to generalizations of the Jordan canonical form

The Jordan normal form for a matrix over an arbitrary field and the canonical form for a pair of matrices under contragredient equivalence are derived using Pták's duality method.     

Construction of systems of differential equations of Okubo normal form with rigid monodromy

For systems of differential equations of the form (xI _n – T )dy /dx = Ay (systems of Okubo normal form), where A is an n × n constant matrix and T is an n × n constant diagonal matrix, two kinds of operations (extension and restriction) are defined. It is shown that every irreducible system of Okubo normal form of semi‐simple type whose monodromy representation is rigid is obtained from a rank 1 system of Okubo normal form by a finite iteration of the operations. Moreover, an algorithm to calculate the generators of monodromy groups for rigid systems of Okubo normal form is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

SMITH NORMAL FORMAL OF DISTANCE MATRIX OF BLOCK GRAPHS

A connected graph, whose blocks are all cliques (of possibly varying sizes), is called a { block graph.} Let D(G) be its distance matrix. In this note, we prove that the Smith normal form of D(G) is independent of the interconnection way of blocks and give an explicit expression for the Smith normal form in the case that all cliques have the same size, which generalize the results on determinants.     

Bounds and perturbation bounds for the matrix exponential

Some new types of bounds and perturbation bounds, based on the Jordan normal form, for the matrix exponential are derived. These bounds are compared to known bounds, both theoretically and by numerical examples. Some recent results on the matrix exponential and the logarithmic norm are also included.