V2EX euclidean norm

Euclidean Norm

Definition / 定义

欧几里得范数(Euclidean norm):向量“长度”的常用度量,等同于把向量各分量平方后求和再开平方;在二维或三维中对应我们熟悉的直线距离。常记为 ‖x‖

Pronunciation / 发音

/jukldin nrm/

Examples / 例句

The Euclidean norm of (3, 4) is 5.
(3, 4) 的欧几里得范数是 5。

In optimization, adding an Euclidean norm penalty can discourage large parameter values and improve generalization.
在优化中加入欧几里得范数惩罚可以抑制参数过大,并提升泛化能力。

Etymology / 词源

Euclidean 来自古希腊数学家 Euclid(欧几里得) 的名字,指“欧几里得几何/空间”中常见的距离概念;norm 源自拉丁语 norma(“准则、规矩”),在数学里引申为“度量长度或大小的规则”。合在一起即“欧几里得空间里定义的长度度量”。

Related Words / 相关词

Literary Works / 文学作品

  • Convex Optimization(Boyd & Vandenberghe)
  • Linear Algebra Done Right(Sheldon Axler)
  • Matrix Analysis(Horn & Johnson)
  • Pattern Recognition and Machine Learning(Christopher M. Bishop)
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