Toeplitz矩阵的性质及其应用

运用矩阵方法,研究了特殊的Toeplitz矩阵A和n阶幂零矩阵在相似变换下的广义逆,得到了Toeplitz矩阵的一些性质,并用这些性质刻画了幂零矩阵A在相似变换下的广义逆的表达形式.     

相似变换下幂零矩阵的{2,3}-逆的表示式

研究复数域上n阶幂零矩阵在相似变换下的{2,3}-逆,运用矩阵块计算方法及Toeplitz矩阵的性质,证明了基于这个幂零矩阵的{2,3}-逆的主要定理,并利用Toeplitz矩阵刻划了幂零矩阵A在相似变换下的所有{2,3}-逆的表达形式.     

r—循环矩阵逆矩阵的插值法证明

本文用插值法给出了[1]中r－循环矩阵逆矩阵计算公式的一个简化证明。     

分块Z-循环矩阵的逆与Moore-Penrose逆的一个算法

本文给出了分块Z-循环矩阵的逆与Moorc-Pcnrosc逆的一个算法。     

对角线元为幂零矩阵的上三角矩阵及其应用

设H_s(s≥2)是复数域瓘上对角线元为幂零矩阵的一个上三角矩阵.利用矩阵方法和数学归纳法,研究并得到了矩阵H_s的幂零性质和有关结论.作为应用,给出了主要定理的一个例子以及分块幂零矩阵H_2的{1}-逆存在的条件及其表示形式.     

“权力”矩阵论

后现代所推崇的物理化的场域概念为我们带来了对权力的吸噬性和复杂性的认识。然而场域的混沌性使我们无法明晰权力运作的真正机制,也难以找到遏制权力的有效途径。权力的矩阵原理开启了权力布控研究的新视角,矩阵的行列图式、运算和秩、逆性质解密了权力的布控、集发、繁殖和归位等多种形态与演变机要。各种力量在简约的纵横对峙中演绎了本性的多维关联,并展现了现代性病灶的多种症候。     

有限域Fq上矩阵的广义逆及矩阵Kronecker积

给出了Fq上矩阵群逆和E-P逆和E-P逆及矩阵Kronecker积的弱广义Schur补定义,并讨论了其相应的特殊性质.     

局部环上一类矩阵广义逆的偏序

设R是局部环,A=P^-1（I^（r）＋D）P∈Mn（R）,其中D=diag{d1,…,dn-r}或D=0,d1,…,dn-r∈M,.研究R上集合意义下广义逆的矩阵偏序A≤^[3]和A≤^[2,3],确定了具有偏序A≤^[3]和A≤^[2,3]的矩阵集Mn（B┇A≤^[3]B）和Mn（B┇A≤^[2,3]B）都不是单点集。     

《广义逆矩阵在线性方程组中的应用》

利用广义逆矩阵研究线性方程组,对于相容的或不相容的线性方程组,均可用同一表达式简明表示方程组的全部解或全部最小二乘解,获得满意而统一的结论。体现出广义逆矩阵在线性方程组理论中的重要意义和作用。本文将较系统地陈述用广义逆矩阵研究线性方程组所得的一系列结果。     

线性变换及矩阵可交换的性质与应用

本文介绍了线性变换及矩阵可交换二者之间的转化方法,并从多角度总结了它们之间的一些重要性质,最后研究了线性变换及矩阵可交换在求证有关数学问题方面的应用.     

左模张量积的同态及其基础环的转移

本文在[1]的基础上，讨论了两个左模张量积的同态，左模和左模张量积的基础环的转移，逆转移。并给出了基础环逆转移的一个同构定理。     

混合边值的逆散射问题

本论文考虑在混合边值情况下的逆散射问题。首先给出散射场满足混合Dirichlet-Robin边界条件的Helmholtz方程的变分公式,其次建立未知边界到已知边界的非线性映射,给出区域导数的定义并利用边界变换计算区域导数值,最后说明此非线性逆散射问题是唯一的。     

二叉树非递归周游算法

本文给出了二叉树的一个非递归周游算法.二叉树采用三重链式存储结构,在算法过程中无须逆转链.     

The Variable Effects of Family Background on the Timing of First Marriage: United States, 1969–1993

Longitudinal data from the Panel Study of Income Dynamics for a sample of 6570 women and men observed between 1969 and 1993 are used to examine historical changes and life-course variation in the effects of family background characteristics on the timing of first marriage. Discrete-time event history analyses reveal that the inverse effect of parental resources (family income and mother's education) on the timing of first marriage has both declined over time and weakens as children age. Historical declines in the effect of parental resources on first marriage timing appear to explain the divergence between Black and White marriage patterns over this period. In contrast, the inverse effect of experiencing a nonintact family structure during childhood on the timing of first marriage remains constant over both historical time and the life course. The implications of these findings for theories of demographic individuation and life-course perspectives are discussed.     

方阵等价于次对角阵的充要条件

给出了次单位阵和次对角阵的基本性质,应用这些性质,得到了方阵等价于次对角阵的充分必要条件.     

Curricular policy as a collective effects problem: A distributional approach

Current educational policies in the United States attempt to boost student achievement and promote equality by intensifying the curriculum and exposing students to more advanced coursework. This paper investigates the relationship between one such effort – California’s push to enroll all 8th grade students in Algebra – and the distribution of student achievement. We suggest that this effort is an instance of a “collective effects” problem, where the population-level effects of a policy are different from its effects at the individual level. In such contexts, we argue that it is important to consider broader population effects as well as the difference between “treated” and “untreated” individuals. To do so, we present differences in inverse propensity score weighted distributions investigating how this curricular policy changed the distribution of student achievement. We find that California’s attempt to intensify the curriculum did not raise test scores at the bottom of the distribution, but did lower scores at the top of the distribution. These results highlight the efficacy of inverse propensity score weighting approaches for examining distributional differences, and provide a cautionary tale for curricular intensification efforts and other policies with collective effects.