Moments for matrix normal variables

In order to obtain moments for matrix normally distributed variables the moment generating function is differentiated by aid of matrix derivatives. Moments of arbitrary order as well as a recursive relation are obtained. Further, some more details are given for the first four moments     

西部农村居民收入流动性结构研究

改革开放以来,中国西部农村收入差距日益扩大。本文基于1989-2011年CHNS提供的西部省区调查数据,研究西部农村居民收入流动性的结构特征和影响因素。运用收入转换矩阵及结构指标分析不同收入阶层的动态演进轨迹,结果表明贫富阶层僵化现象严重,中间阶层趋于脆弱化。用多分类逻辑模型揭示收入结构、支出结构和职业特征对收入流动性的影响显著。从制度和体制上改善西部农村收入流动性结构确实已刻不容缓。     

A pseudo restricted MLE under multivariate order restrictions and its algorithm

Abstract

It is shown in this paper that a quasi order for the vectors in R^p is a cone induced if and only if the order is preservable under limits and under linear combinations with non-negative coefficients. For the mean vectors in MANOVA subject to the restriction of simple ordering, a pseudo restricted MLE is proposed. This estimator is a matrix projection onto a closed convex set inside the restricted domain. An algorithm for the pseudo restricted MLE is developed, that computes the matrix projections using only vector projections.     

矩阵多项式的逆

本文证明了数域Ｋ上矩阵Ａ的多项式的逆仍是Ｋ上矩阵Ａ的多项式,并给出了求矩阵多项式的逆的方法．     

实四元数体上的Patel-Toda不等式及改进

本文证明了一些自共轭实四元数矩阵的不等式,推广、改进了Hermitian矩阵的Patel-Toda不等式。     

矩阵Liouville公式

多重积分中的Liouville公式被文[1][2]进行了推广,本文中对[1][2]中的积分变量改为正定列满秩矩阵,也得到了相应的Liouville公式,它将包含[1][2]中的Liouville公式。     

Balanced arrays of strength 4 and balanced fractional 3m factorial designs

A connection between a balanced fractional 2^m factorial design of resolution 2l + 1 and a balanced array of strength 2l with index set {μ₀, μ₁,…, μ_2l} was established by Yamamoto, Shirakura and Kuwada (1975). The main purpose of this paper is to give a connection between a balanced fractional 3^m factorial design of resolution V and a balanced array of strength 4, size N, m constraints, 3 levels and index set {λ_l0l1l2}.     

齐次矩阵微分方程解的几何描述

以二维齐次矩阵微分方程为例,给出了其解的几何描述.     

“线性代数,多重线性代数与矩阵论”论著者的学术群落

本文统计分析了《中国数学文摘》中15类的文摘情况,初步得出我国“线性代数、多重线性代数与矩阵论”的论文著者的活跃著者群。     

一元n次多项式根的圆环覆盖定理

本文的主要结果是利用相容矩阵范数的性质给出了一元ｎ次多项式根的圆环覆盖定理，即一元ｎ次多项式的所有非零复根必全都落在复平面上同一个圆环区域内．特别，ｎ次二项式的所有非零复根必都落在同一个圆周上．这一结果，可以改进盖尔斯果林（Ｇｅｒｓｓｇｏｒｉｎ）的圆盘覆盖定理的结果．