矩阵方程AXAT=C的对称斜反对称解

设A∈Rm×n,C∈Rm×m给定,利用矩阵的广义奇异值分解和对称斜反对称矩阵的性质,得到了矩阵方程(1)AXAT=C存在对称斜反对称解的充要条件和通解表达式;证明了若方程(1)有解,则一定存在唯一极小范数解,并给出了极小范数解的具体表达式和求解步骤.     

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

In this note,we consider the backward errors for more general inverse eigenvalus prob-lems by extending Sun‘‘‘‘s approach.The optimal backward errors defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution,and the upper and lower bounds are derived for the optimal backward errors.The results may be useful for testing the stability of practical algorithms.     

The optimal preconditioner of strictly diagonally dominant <Emphasis Type="Italic">Z</Emphasis>-matrix

In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained show that the bigger the parameter k is（i.e., we select the more upper right diagonal elements to be the preconditioner）, the less the spectral radius of iterative matrix is. A numerical example generated randomly is provided to illustrate the theoretical results.     

THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS （AX- B, XC- D）

In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.     

命题模糊逻辑系统П和God中理论的相容度与下真度的计算公式（Ⅱ）

讨论命题模糊逻辑系统П和God中理论相容度与下真度的计算问题。引入逻辑公式的核、零核及理论的核的新概念，得到命题模糊逻辑系统Ⅱ和God中理论相容度与下真度的计算公式，给出理论不相容的新的充要条件。     

基于核心矩阵的线性规划块转轴算法研究

本文在线性规划问题核心矩阵概念的基础之上,对单纯形算法的块转轴规则进行了深入的研究.在线性规划的Kuhn-Tucker条件基础之上,证明了单纯性算法块转轴规则的理论可行性,并在文章中给出了块转轴规则的理论算法,为转轴规则的研究提出了一个新的方向.     

关于brauer定理的注记

本文讨论了经典的ｂｒａｕｅｒ定理中的错误，指出产生错误的原因，并给出修正的结果．     

V2的泡利自旋阵表示

在用矩阵法求解二维伊辛模型时，需要用泡利自旋矩阵来表示Ｖ２矩阵，本文给出该表示的一种推导方法。     

P—对称等带宽带状方程组的改进平方根法

本文将改进平方根法拓广到求解Ｐ－对称等带宽带状方程组，并给出相应的矩阵压缩存储方法及ＦＯＲＴＲＡＮ过程描述。