positive definite

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

这些性质类似于通常的半正定矩阵及正定矩阵的性质。

However, the traditional trust region subproblem may meet difficulty. The Hessian matrix of the trust region subproblem may not be positive definite. In this case, the convergence rate of some trust region methods is only linear.

但传统的信赖域算法存在如下弱点：当信赖域子问题的海森矩阵不正定时，数值计算上存在一定困难，此时有些算法只具有线性收敛速度。

Best approximation solution for α-symmetric positive semi-definite matrix on a linear manifold

线性流形上α-对称半正定阵的最佳逼近解

Relations Among Some Kinds of Positive Definite Matrix Classes and Positive Stable Matrix Classes

一些正定矩阵类及正稳定矩阵类之间的关系

The Character an the Application for Semi-definite Positive Quadratic Form

半正定二次型的性质及应用

A unified simple condition for stable matrix, positive definite matrix and M matrix is presented in this paper.

本文给出了一个判定矩阵稳定、正定以及为M矩阵的统一简化条件。

Based on the definitions of generalized positive definite matrix, a further study of it is made in the present paper, and several new results are obtained as a consequence.

提出了超正稳定的概念，讨论了实对称正定、亚正定、良广义正定、广义正定、超正稳定及正稳定矩阵类之间的关系，得到了若干确定的结果。

A Class of Positive Semi-definite Sextic Polynomial and Its Linearity Properties

一类半正定六次型及其线性性质

And then based on some properties of Metzler matrix, the positive definite problem of delay Volterra integro-differential equation is discussed in intensity continuous semi-group.

然后，利用Metzler矩阵的一些性质在强连续半群上讨论时滞Volterra积分微分方程的正定性问题。

The Positive Semi-definite of Gram Matrix and it's Application

格拉姆（Gram）矩阵的半正定性及其应用

Relationship between generalized positive definite matrix and stable matrix and Minkowski matrix

广义正定矩阵与稳定矩阵、M-矩阵的关系

Using the notion of the Non-Hermite positive definite matrix and its properties, some new sufficient and necessary conditions of positively stable matrix are obtained.

利用非Hermite正定矩阵的概念及性质，获得了正稳定矩阵几个新的充要条件。

Study on Bounds on Determinants for Kronecker Products and Hadamard Products of Positive Definite Self conjugate Matrices

关于正定自共轭矩阵的Kronecker乘积与Hadamard乘积的行列式的界限

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

一种基于加权F-范数的半正定矩阵的逼近方法

A Unified Simple Condition for Stable Matrix, Positive Definite Matrix and M Matrix

判定矩阵稳定、正定以及为M矩阵的统一简化条件

The method can guarantee global stability without searching a common positive definite matrix.

该方法无需求正定矩阵就能保证系统全局稳定.

Some properties of adjoint matrix are discussed. The properties are symmetry, antisymmetry, positive definite, positive semi-definite, orthogonal and characteristic value.

讨论了伴随矩阵在对称、反对称、正定、半正定、正交、相似和特徵值等方面的性质。

If a symmetrical matrix is positive definite, the determinants of all its minors are also positive.

如果对称矩阵是为正定者, 它的所有子式的行列式也都是正的.

Results linear complementary problem have unique solution when M is generalized positive definite matrix.

结果得到了当M是广义正定矩阵时,线性互补问题存在唯一解.

Lagrange multiplier method provides necessary conditions for the constrained extreme value of the function of many variables, so this paper, based on the theory of positive definite quadratic form, proves the sufficient condition for the constrained extreme value of the function of many variables.

拉格朗日乘数法给出了多元函数条件极值的必要条件，本文利用正定二次型理论证明多元函数条件极值的一个充分条件。

Non-Hermite positive definite matrix and positively stable matrix

非Hermite正定矩阵与正稳定矩阵

Moreover, the condition is also sufficient if the positive definite matrix is included in this set.

当这个集合中包含有正定矩阵时, 上述必要条件也是充分的.

Positive semi-definite matrices are positive definite if and only if they are nonsingular.

正半定矩阵是正定的,当且仅当它们是非奇异矩阵.