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.
本文主要说明在各种情况下，如何正确写出矩阵，并解决了基矢和矢量变换中的有关问题。
This paper mainly explains how to Corectly Write the matrices under kinds of circumstances, and resolves concerning problems in the transformation of basic vector and vectors.
本文用欧几里得算法，给出求解基矢变换对应矩阵的解析表达式。
An analytical method to find correspondence matrix for basic vector transformation is given by using elementary theory of numbers.
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