定义了正规矩阵，并给出了判断正规矩阵正定的若干方法。
This paper gives the definition regular matrix and offers several methods for deciding the regular matrix definite.
然而，目前国内外有关协方差矩阵正定性的研究结果并不多，并且大多是集中在连续型样本协方差矩阵方面。
However, there have been few outcomes about the positive definitiveness of covariance matrix, most of which have been restricted to the Covariance-matrix of continuous sample.
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。
Results linear complementary problem have unique solution when m is generalized positive definite matrix.
进而将积分方程形式的特征值问题转化为无穷阶正定对称矩阵的标准特征值问题。
And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order.
损伤弹性矩阵的计算符合连续介质力学的对称、正定等一般原理。
The calculation method of elasticity matrix is in accordance with the principles of symmetry and positive definite in continuum mechanics.
利用构造正定矩阵的方法，给出了判别不确定时滞系统鲁棒稳定的几个新结果，同时讨论了这类系统的稳定度。
By using the method of constructing positively definite matrix, some new results for robust stability of uncertain time_delay systems are derived, and the stability degree is also discussed.
本文以半正定矩阵为工具，统一了一类几何不等式，获得了一个相当一般的结果。
In this paper, we use semi-definite matrix to generalize geometric inequalities and obtain a general result.
给出了实部半正定矩阵的一种判定方法，并给出了该判定方法的算法。
A criterion for the real part positive semidefiniteness matrix is presented, and the algorithm for this criterion is given.
希望为广义正定矩阵概念的规范化探出一条新路。
It wishes to find a new way for normative research into the concept of generalized positive definite matrix.
该方法的主要优点在于其迭代矩阵总保持对称正定。
The main advantage of the proposed method is: the iterative matrix is symmetric and positive definite at ea ch iteration.
借助矩阵的合同变换法，给出了化实二次型为标准形的方法、求标准正交基的方法，并给出了正定二次型判定定理的新证明。
By means of congruent transformation in matrix, the method of transforming real quadratic form into standard form and the method of normal orthogonal basis are given in this paper.
指出非对称广义正定矩阵的主子矩阵一般不是非对称广义正定矩阵。
The principal submatrix of the asymmetrical generalized positive definite matrix is not asymmetrical generalized positive definite matrix in general.
用这个方法修正的刚度矩阵不仅满足特征方程，而且是唯一的对称半正定矩阵。
The stiffness matrix corrected by the method not only satisfies the characteristic equation, but also is the unique symmetric positive semidefinite matrix.
直接法中的平方根法，就是利用对称正定矩阵的三角分解而得到的求解对称正定方程组的一种有效方法。
Square root method is one of direct methods, which is an effective method for the solution of symmetrical positive liner equations through triangle decomposition of symmetrical positive matrix.
正定矩阵在矩阵论中占有十分重要的地位，在实际中也有广泛的应用价值。
Positive definite matrix occupies a very important position in matrix theory, and has great value in practice.
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.
本文给出了用低阶矩阵来判定高阶矩阵的广义对称正定的判定定理。
A theorem to determine the generalized positive definiteness of high-order matrices by low-order matrices is given.
讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。
Some sufficient and necessary conditions of the full symmetric real matrix is full definite matrix are discussed.
对给定的特征值和对应的特征向量，提出了对称正交对称半正定矩阵逆特征值问题及最佳逼近问题。
From given eigenvalues and eigenvectors, the inverse eigenvalue problem of symmetric ortho-symmetric positive semi-definite matrices and its optimal approximate problem were considered.
当协方差矩阵非正定时，要么存在套利机会，要么存在有效子集（即有多余的证券存在）。
We concluded that the covariance matrix is nonpositive definite, there is either arbitrage opportunity or efficient subset.
本文给出的半正定二次型的若干判别方法及半正定对应系数矩阵的一些相关性质。
The paper gives a number of methods for differentiating half positive definite quadratic form and some relevant properties in respect to half positive definite corresponding coefficient matrix.
利用实对称矩阵的半正定之等价条件给出了复正半定矩阵的几个等价条件。
Some equivalent representations of complex positive semi definite matrices are given by using equivalent conditions of positive semi definite of real symmetric matrix.
我们讨论了次正定矩阵的判别法，给出了次正定矩阵的行列式的一个不等式。
The necessary and sufficient conditions of metapositive definite matrices are discussed and an inequality for the determinants of metapositive definiter matrices is given.
最后得到一个矩阵型的位移广义本征值方程，刚度矩阵对称、正定。
Finally a displacement generalized eigenvalue equation is obtained, in which the stiffness matrix is symmetric and positively definite.
给出实矩阵的广义谱分解式，讨论广义正定实矩阵的特征根的一些性质。
In this paper, we give a general spectral resolution of real matrix and some properties eigenvalue of a general positive definite real matrix.
本文考虑当系数矩阵为正定对称矩阵，H阵及L阵情况下TOR型方法的收敛性。
We consider the convergence of TOR-Type method under the conditions when the coefficient matrices are positive definite symmetric matrices, H-mat - rices, L-matrices.
当特征根难以求出而特征根的对称式易求时，半正定矩阵的算术平方根可直接由矩阵的本身的性质来表示。
On the other hand, square roots of semi-positive matrices can be expressed by the symmetric expression of eigenvalues, if the eigenvalues of semi-matrices are difficult to compute.
本文给出了全正定矩阵的概念，讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。
In this paper the concept of the full definite matrix is given, some sufficient and necessary conditions of the full symmetric real matrix is full definite matrix are discussed.
本文给出了全正定矩阵的概念，讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。
In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.
本文给出了全正定矩阵的概念，讨论了全对称实矩阵是全正定矩阵的几个充分必要条件。
In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.
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