The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.

研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基。

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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.

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。

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