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.
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.
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.
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