整环上几类矩阵空间的保持伴随矩阵线性算子

本文刻画了整环上的全矩阵空间、对称矩阵空间和上三角矩阵空间上保持伴随矩阵的线性算子的结构。     

拓扑线性空间上一类矩阵变换

对拓扑线性空间之间的一类映射(包括线性算子全体和一类非线性算子)所作矩阵得到一系列基本的矩阵变换定理.     

相似变换矩阵的空间结构探讨

给定 n阶方阵及其若当矩阵 ,讨论所有与该若当矩阵可交换的矩阵空间的结构 ,得出方阵的所有相似变换矩阵的空间结构 .     

幂幺矩阵的充要条件

研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.     

关于矩阵秩的一个不等式

对任意矩阵 M,用 r( M)表示 M的秩。熟知 ,矩阵的秩是矩阵的一个重要不变量 ,对矩阵的加法和乘法 ,我们有下面两个基本的不等式。(一 )设 A、B是两个 m× n矩阵 ,则r( A +B)≤ r( A) +r( B) ( 1 )　　 (二 )设 A、B分别是两个 m× n、n× l矩阵 ,则r( A) +r( B) -n≤ r( AB)≤ min{ r( A) ,r( B) }它通常被称为 Sylvester不等式。对这两个不等式 ,有不同的证明和理解 ,见 [1、2 ]。在本文里 ,我们要结合矩阵的满秩分解 ,用不等式 (二 )来研究不等式 (一 ) ,从中给出 r( A+B)≤ r( A) +r( B)的一个推广形式。本文所需的矩阵知识是基…     

对合pascal矩阵

研究对合pascal矩阵Un,根据它的特殊结构,给出对合pascal矩阵Un和UnT的特征向量.最后还分别得到了Un和UnT的对应特征值1和-1的特征子空间.     

浅析基矩阵在线性代数教学中的应用

主要研究基矩阵在线性代数教学中的应用.具体讨论基矩阵在矩阵乘法运算的几何意义、乘法运算律、线性空间等方面的教学中的应用.旨在提高线性代数的教学质量.     

相似变换矩阵的空间结构探讨

结定n阶方阵及其若当矩阵，讨论所有与该若当矩阵可交换的矩阵空间的结构，得出方阵的所有相似变换矩阵的空间结构。     

矩阵逆与行列式的新型求法

本文将根据线性空间基与基之间的过渡矩阵来求两类矩阵的逆,并且由此过程得到范德蒙矩阵的逆与行列式的具体值,也由此衍生出来关于复数的一些相关结论．     

扩张矩阵的一些性质

研究了相关于扩张矩阵A的扩张球和拟范数的一些性质.首先通过具体实例及欧氏范数关于A的上下界估计指出扩张矩阵与经典球及欧氏范数匹配不佳,但欧氏范数相关于A仍能保持全局伸缩性.其次研究了相适应于扩张矩阵的扩张球和拟范数关于伸缩性、凸性、可积性、微分估计及傅里叶变换的一些性质.最后通过欧氏范数与相关于扩张矩阵的拟范数的不等式估计证明了相关于拟范数的两类施瓦茨函数空间和相关于欧氏范数的经典施瓦茨函数空间都是等价的.     

一类系统矩阵A的行列单调性

本文讨论了极大代数意义下矩阵的行列单调性,给出了一类系统矩阵A的行列单调性.     

一类特殊模糊矩阵方程的简便求解

给出了一类特殊模糊矩阵方程的简便且实用的求解方法.     

On the Matrix Equations of Higher Degrees

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线性矩阵方程的行列式求解法

本文讨论了线性矩阵方程AXB= C (A,B可逆)的用行列式表示的求解公式,并附带指出它是Cram er法则的重要推广.     

体上二次矩阵方程的解

本文得到了体上二次矩阵方程XAY= B有解的充要条件.并给出了当r(A)= r(B)时矩阵方程XAY= B的通解.     

An Arithmetic for Matrix Pencils: Theory and New Algorithms

This paper introduces arithmetic-like operations on matrix pencils. The pencil-arithmetic operations extend elementary formulas for sums and products of rational numbers and include the algebra of linear transformations as a special case. These operations give an unusual perspective on a variety of pencil related computations. We derive generalizations of monodromy matrices and the matrix exponential. A new algorithm for computing a pencil-arithmetic generalization of the matrix sign function does not use matrix inverses and gives an empirically forward numerically stable algorithm for extracting deflating subspaces.Some of this work was completed at the University of Kansas. Partial support received by Deutsche Forschungsgemeinschaft, grant BE 2174/4-1.This material is based upon work partially supported by the DFG Research Center “Mathematics for Key Technologies” (MATHEON) in Berlin, the University of Kansas General Research Fund allocation 2301062-003 and by the National Science Foundation under awards 0098150, 0112375 and 9977352.     

Optimal bounded-thrust space trajectories based on linear equations

Necessary and sufficient conditions for solution of the general minimum-fuel linear bounded-thrust spacecraft trajectory problem are presented in terms of fundamental matrix solutions and their inverses. This work is rigorous, generalizes and unifies many known results for specific problems, and also presents a new necessary condition. Finally, an application is presented for a spacecraft rendezvous near a general Keplerian orbit in which the linearized equations of motion are nonautonomous. A fundamental matrix solution is found and inverted, solving this class of problems.     

Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates

This paper considers the problem of stabilization for a class of stochastic Markov jump distributed delay systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov function, a state memory feedback controller is designed to guarantee that the resulted closed-loop constrained systems are mean-square stochastic asymptotically stable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Am×n矩阵的加边矩阵的奇异性问题

给定m×n阶矩阵A,我们给出了它的加边矩阵M=[A B C O] (1)为非奇的充分必要条件。其中O为r₁×r₂阶零矩阵。把M的逆矩阵记为分块形式M^-1=[A₁ B₂ C₃ O₄]其中C₁为n×m、C₂为n×r₁、C₃为r₂×m、C₄为r₂×r₁阶矩阵。在一定条件下,我们证明了其中的C₁为A的广义逆矩阵A⁺。     

Chaos in M(atrix) theory

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N = 2 supersymmetric Yang—Mills theory is also discussed. We demonstrate that after the separation of “slow” and “fast” modes there is a singular contribution from the “slow” modes to the Hamiltonian of the “fast” modes.