> For the complete documentation index, see [llms.txt](https://blog.cweihang.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://blog.cweihang.io/ml/trick/l2_normalize.md).

# L2 Norm与L2 normalize

## L2 Norm

L2 Norm是向量一个L2模，是一个实数，也称L2范数，二范数

$$norm(x) = \sqrt{x\_1^2+x\_2^2+...+x\_n^2 }$$

## L2 Normalize

L2归一化，是对单个向量的各个元素做归一化的手段，使得向量x变换后的结果x'的L2 norm为1

$$1 = norm(x')=\frac{\sqrt{x\_1^2+x\_2^2+...+x\_n^2 }}{norm(x)}$$ $$=\sqrt{\frac{x\_1^2+x\_2^2+...+x\_n^2}{norm(x)^2}}$$ $$=\sqrt{(\frac{x\_1}{norm(x)})\_2+(\frac{x\_2}{norm(x)})\_2+...+(\frac{x\_n}{norm(x)})\_2}$$ $$=\sqrt{x\_1^2'+x\_2^2'+...+x\_n^2'}$$

即： $$x'\_i =\frac{x\_i}{norm(x)}$$


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