半正定矩阵

若对所有n维复向量X都有Re（x~HAx）≥0，则称A为半正定矩阵；

A is called a positive semidefinite matrix , if for all x ∈ Cn , Re ( XHAX )≥ 0 ;

平方为复半正定矩阵的一个等价表征

Equivalent representations of squares being complex positive semidefinite matrix

一些半正定矩阵的迹不等式及相关的RichardBellman问题

Some Trace Inequalities for Nonnegative Definite Matrices and Related Richard Bellman 's Problems

半正定矩阵Hadamard积的不等式

Inequalities for the Hadamard Product of Positive Semidefinite Matrices

讨论矩阵在闭凸锥上的最佳逼近及其数值算法，在对称半正定矩阵集上，给出了最佳逼近数值算法的MATLAB程序和数值例子。

In the case of the set of semi-definite symmetric matrices , a MATLAB program and a numerical example for the optimal approximation numerical algorithm are given .

复半正定矩阵的Hadamard乘积与Kronecker乘积

Hadamard Product and Kronecker Product of Positive Semidefinite Complex Matrices

利用特征根的Lagrange插值多项式，给出了半正定矩阵算术平方根的表示，即公式解，避免了求过渡矩阵的繁琐过程。

Representations of square roots of semi-positive matrices by Lagrange 's interpolation polynomial , namely formula representations were given , which will avoid the computation of transfer matrix .

算法用对称半正定矩阵作为元素目标函数的Hessian阵的近似，使得其和仍然保持目标函数的Hessian阵的某种稀疏性。

In the method , the symmetric positive semidefinite matrices are updated to approximate the Hessian matrices of the elemental objective functions and their sum to approximate the Hessian matrix of the objective function .

对矩阵的低秩Hankel半正定矩阵逼近，采用特殊的分解形式，可将其转化为一个无约束的优化问题进行求解，本文应用拟牛顿方法求解无约束优化问题。

Based on the special decomposition of Hankel matrix , we can transform the problem of approximating a given matrix with a positive semidefinite real Hankel matrix of lower rank to a smooth unconstrained optimization problem .

同时研究了特殊矩阵为半正定矩阵的充分条件，从而部分回答了Murthy猜想。

We further more research the condition of special matrix being semi positive definite matrix and partly solve the sufficient conditions of Murthy guesses .

一种基于加权F-范数的半正定矩阵的逼近方法

An Approximation Method of Positive Semi-definite Matrix Based on Weighted F-norm

复半正定矩阵的奇异值不等式

Some inequalities for singular values of complex positive semidefinite matrices

半正定矩阵算术平方根的表示

Square root s representations of semi - positive matrices

实部半正定矩阵反问题

The inverse problems for real part positive semidefinite matrix

关于对称不定和广义半正定矩阵的扰动分析

Perturbation Analysis on Symmetric Indefinite and Generalized Semi-Positive Matrices

矩阵和真半正定矩阵的概念，从而定义了新的矩阵类；

Martrix and proper - semi positive definite matrix .

对称正交对称半正定矩阵逆特征值问题

Inverse Eigenvalue Problem of Symmetric Ortho-Symmetric Positive Semi-Definite Matrices

关于对称半正定矩阵线性方程组解法的注记

Solution of linear equations for symmetric semi-positive definite matrix

实对称半正定矩阵的三角（LL~T）分解

Triangular ( LL ~ T ) Decomposition of Real Symmetric Positive Semidefinite Matrix

具对称半正定矩阵线代数方程组的直接法

The direct method for the solution of linear algebraic equations with semi-positive definite matrix

关于半正定矩阵迹的几何&算术平均不等式

The geometric-arithmetric-mean inequality for positive semidefinite matrix traces

关于两个四元数自共轭半正定矩阵乘积的特征值估计

On the Estimation of Eigenvalues of Product of two Self-Conjugate Semi-Positive Definite Quaternions Matrices

欧几里得距离矩阵与半正定矩阵的关系欧几里德不一定全对。

Connections Between Euclidian Distance Matrix and Positive Semidefinite Matrix Euclid was not always right .

这些性质类似于通常的半正定矩阵及正定矩阵的性质。

These properties are similar to properties of positive semi-definite matrices and positive definite matrices .

对称半正定矩阵的二级多分裂

Two-stage Multisplitting of Symmetric Positive Semidefinite Matrices

复半正定矩阵的标准形及行列式模的不等式

The canonical form and inequalities of the norm of determinant for complex semidefinite positive matrix

半正定矩阵乘积的特征值

The Eigenvalues of Positive Semidefinite Matrices

广义半正定矩阵

Generalized Positive Semidefinite Matrices

本文讨论谱约束下实对称半正定矩阵束的最佳逼近问题，指出一般算法。

This paper is concerned with the problem of real symmetric positive semidefinite matrix pencil under spectral restriction .

实对称半正定矩阵LDL~T分解的存在性与唯一性及有关问题

On the existence and uniqueness of ldl ~ t decomposition of real symmetric nonnegative definite matrices and related problems