关于广义积分在判别矩阵正定性方面的应用

用实例说明用广义积分判别某些矩阵的正定性

对广义正定矩阵的进一步研究

广义的正定矩阵除了具有常规正定矩阵的性质之外,还有很多自己特有的性质。而且,初步推广的正定矩阵和广义的正定矩阵具有很多相同的性质。

条件极值的一个充分条件

设函数f(x,y,z)与φ(x,y,z)在空间区域Ω上具有二阶连续偏导数,讨论了函数ω=f(x,y,z)在条件φ(x,y,z)=0下取得极值的充分条件及其推广.

单位法矢在不等式证明中的妙用

大家知道,有一类不等式的证明是可以运用实二次型矩阵的正定性来解决的.而高阶矩阵的正定性判定也往往不很容易,本文介绍单位位向量来解决其中的一类问题.

Some new bound estimates of the Hermitian positive definite solutions of the nonlinear matrix equation X^s+ A~*X^(-t) A = Q

The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.