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.
通过给出几个实例，介绍了利用二次型的半正定性证明不等式的方法。
The author introduce the method of applying positive semi-definite quadratic form to prove inequality by giving several examples.
现有的大多数分类问题都能转化成一个正定二次规划问题的求解。
Most existed classification problems can be converted into a positive definite quadratic program.
给出了一个求解正定二次规划的区域分解方法。
A region decomposition method to solve a positive definite quadratic programming is presented.
在第二章，我们提出了一种解决具有原方块角形结构正定二次规划问题的分解协调算法。
In chapter 2, we presented a method for solving positive definite quadratic programming with coupled-block structure.
建立了道路识别问题的数学模型并将上述问题与一个不等式约束的正定二次规划问题相联系。
A mathematic model of road identification problem is provided and the problem is related with a positive definite quadratic programming problem with inequality constraints.
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.
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.
在第三章，我们提出了一种解决具有边界约束的正定二次规划问题的对偶方法。
In chapter 3, we presented a dual method for solving positive definite quadratic programming with box constraints.
给出了次半正定矩阵的递归判别法，讨论了次半正定矩阵的次合同标准形。
Meanwhile the paper set up a new method to gain the standard form of a real symmetry matrix.
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ，定义了二元齐次多项式的正定性 ，并基于定义给出了二元函数极值的一个充分条件。
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions, in which a new sufficient condition and its concise proof when critical case is given.
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ，定义了二元齐次多项式的正定性 ，并基于定义给出了二元函数极值的一个充分条件。
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions, in which a new sufficient condition and its concise proof when critical case is given.
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