光学系统的等效变换

本文在普遍情况下使用矩阵方法详细讨论了光学系统的等效变换,证明光线变换矩阵为的光学系统当C≠0时可等效为一个薄透镜,当C=0时等效为一个薄透镜组。文中所得结果能用于分析光线或光束通过复杂光学系统的变换和多元件光腔的问题。     

关于“长阵方程AXB＋CYD＝E的通解”的注记

文[1]利用矩阵的加逆给出了矩阵方程AXB＋CYD＝E解的相容性，唯一性及通解，本文指出，文[1]的结果可利用矩阵的减号逆写得更一般些，而且纠正了文[1]的几处错误。     

单系统齐次和非齐次微分方程解的有界性

本首先研究了单系统齐次微分方程系数矩阵与解的关系；并给出了解的有界性与特征函数之间的一般关系，最后讨论了非齐次线性方程解的有界性。     

矩阵的γ阶相似性

本首次给出了两个矩阵γ阶相似的概念，并得到了矩阵γ阶相似的充要条件及γ阶相似下关于矩阵的秩、特征多项式的一些性质，从而进一步丰富了矩阵的相似理论。     

STABLE DOUBLE LR ALGORITHM AND ITS ERROR ANALYSIS

In this paper, the normative matrices and their double LR transformation with origin shifts are defined, and the essential relationship between the double LR transformation of a normative matrix and the QR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double LR algorithm for double LR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double LR algorithm for normative matrices is only four sevenths of the rational QR algorithm for reed symmetric tridiagonal matrices.     

设计结构矩阵在复杂产品协同设计过程的应用

将矩阵方法应用到复杂产品的开发过程中，用DSM（设计结构矩阵）量化表达复杂产品的设计流程，并通过DSM的分析与重构进行复杂产品的协同设计规划，以缩短产品设计周期，降低开发成本。     

BRILL－NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.     

紧矩阵量子群G的余表示与其对偶量子群(A)的关系

设 G=（A,△）为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过（A,△）的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C＊-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim（α）=dim（pα）.     

用矩阵讨论多元函数的极值问题

利用矩阵给出了多元函数在稳定点取极值的充分条件，提出了解决两类极值问题的代数方法。     

环上矩阵的分解

将复数域及四元数体上矩阵的积因子分解推广到上矩阵，并指出[1]中的定理2的证明是错误的，由此可知[1]中定理2的结论不成立。