1) complex positive definite matrix
复正定矩阵
1.
The positive definite properties of schur complement for complex positive definite matrix are discussed by using the concept, their some determinantal inequations are established, a few results of recent researches are improved and generalized.
给出了局部Hermite阵的概念 ,利用它研究了复正定矩阵的Schur补的正定性 ,并建立了一系列行列式不等式 ,改进并推广了Minkowski,Ostrowski_Taussky ,屠伯埙 ,李炯生等的一些著名结果。
2.
Some Determinantal inequalities on complex positive definite matrix are also presented.
本文指出了文献[3-6]中的一些不正确的结论,并给出了复正定矩阵的行列式不等式。
2) positive definite complex matrix
复正定矩阵
1.
In this paper,author discusses the necessary and sufficient conditions for the positive definite complex matrix solution of the inverse problem of matrix equation XAX=B with the positive definite of the partition complex matrices,moreover,gives out the expression of the solution.
本文利用分块矩阵的复正定性,讨论了矩阵方程XAX=B的反问题有复正定矩阵解的充要条件,进而给出其解的形式。
2.
In this paper, we have given several properties of determinant and trace for positive definite complex matrix, and improves some existing results.
本文绘出了复正定矩阵的迹和行列式的几个性质，改进了现有的一些结果。
3) complex positive definite matrix
正定复矩阵
1.
Two inequalities of complex positive definite matrix determinant;
正定复矩阵行列式的两个不等式
2.
An inequality of a model of the complex positive definite matrix determinant;
关于正定复矩阵行列式模的一个不等式
3.
In this paper, some important inequalities on norm of determinent of complex positive definite matrix and its Schur complement are obtained.
给出关于正定复矩阵及其Schur补的行列式的模的一组不等式 。
4) Positive definite complex matrix
正定复矩阵
1.
When the concept of the generalized positive definite complex matrix is introduced,we should also discuss corresponding properties and structures which are undoubtedly meaningful to enrich the content of the matrix theory.
正定复矩阵是矩阵论中的一个重要概念,人们已经掌握了它的若干性质与结构。
2.
As one of its application,we prove a number of important inequalities of the determinantal modulus of a positive definite complex matrix.
本文得到正定复矩阵的一个新的判别定理。
3.
Some equivalent conditions of the positive definite complex matrix are given.
给出正定复矩阵的若干个等价条件，讨论了正定复矩阵的主子阵的特征值、行列式模的不等式及正定复矩阵的Ｓｃｈｕｒ补。
5) complex metapositive sub-definite matrix
复次亚正定矩阵
1.
The sub-definite of matrix generalize Fischer s results on a positive definite matrix to the complex metapositive sub-definite matrix,to get a new conlusion.
笔者讨论了复次亚正定矩阵的一些性质及行列式不等式,解决A,A n2的上界、下界问题,进一步研究了分块矩阵的次正定性,将Fischer关于正定矩阵的结果推广到复次亚正定矩阵上,从而得到新的结论;利用A A次正定性,推导出Khatri-Rao乘积的次正定性。
6) complex metapositive definite matrix
复亚正定矩阵
1.
On several inequalities of complex metapositive definite matrix;
关于复亚正定矩阵的几个不等式
2.
The properties of metapositive definite of complex normal matrices are discussed,and a series of necessary and sufficient conditions under which of the product two complex matrices will be a complex metapositive definite matrix is given,and some new results are gained.
研究了复正规矩阵的亚正定性,给出了复矩阵之积为复亚正定矩阵的一系列充要条件,获得了一些新的结果;改进并推广了Ky Fan Taussky定理、Fejer定理等。
补充资料：正定矩阵
设m是n阶实系数对称矩阵， 如果对任何非零向量
x=(x_1,...x_n) 都有 xmx^t>0，就称m正定。
正定矩阵在相似变换下可化为标准型， 即单位矩阵。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条