基于Hermite矩阵的几类重要不等式

笔者给出了Hermite矩阵特征值的Wieland - Hoffman型不等式,研究了Hadamard乘积下的矩阵迹的Cauchy型不等式、H（o）lder型不等式、Minkowski型不等式以及几何平均不等式.

多元函数凹凸性的定义和判别法

将一元函数凹凸性的二阶导数判别法推广到二元函数和多元函数,应用多元函数二阶导数构成的海赛矩阵来判别多元函数的凹凸性,并通过实例说明一元函数凹凸性推广到多元函数时的某些不同之处.

The Monotonicity Problems for Generalized Inverses of Matrices in H (n, ≥)

On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.

四元数方阵的GH合同标准形与同时对角化

给出半正定与正定四元数阵的GH合同标准形,以及两半正定(正定)四元数阵GH合同的充要条件.并给出两自共轭四元数阵(其一为半正定)的同时GH合同简化形,由此得到两自共轭同时对角化问题的一些结果.

有关矩阵广义逆AT,S2的惯性指数及其应用（英文）

建立了某些有关矩阵广义逆AT,S^(2)表达式的惯性指数公式。基于所得惯性指数,作为应用研究了矩阵的正定(半正定)性、负定(半负定)性。给出了一些矩阵分别为正定矩阵、半正定矩阵、负定矩阵、半负定矩阵的充分必要条件。

Hermitian Positive Definite Solutions of the Matrix Equation X ＋ A^＊X^-qA = Q （q≥1）

In this paper,Hermitian positive definite solutions of the nonlinear matrix equation X + A*X-qA = Q(q ≥ 1) are studied.Some new necessary and sufficient conditions for the existence of solutions are obtained.Two iterative methods are presented to compute the smallest and the quasi largest positive definite solutions,and the convergence analysis is also given.The theoretical results are illustrated by numerical examples.