借助内积关系，给出了欧氏空间的变换是线性变换的两个充要条件，并由此得到一些相关结论。

By the relation transvection, we obtain two necessary and sufficient conditions for the transformation being linear transformation in Euclid Spaces, and out of it, we have got some conclusions.

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镜面反射是欧氏空间中一类很重要的线性变换，在几何空间中有着极其形象的解释。

The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space.

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利用长度关系给出了欧氏空间的变换为对称变换的若干个充要条件。

A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.

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