二次型化标准形常采用配方法，而二次型化标准形等价于它的矩阵合同对角化，文中利用初等矩阵和初等变换之间的关系。

Method of completing square is often used when transforming a quadratic form into a normal one, whose process is equivalent to making the relevant matrix contract diagonal.

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线性二次型最优调节器的权矩阵选择问题至今尚未得到较好解决。

The matrices of linear quadratic optimal regulators not yet be resolved perfectively.

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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.

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