V2EX normed space

Normed Space

定义 Definition

赋范空间:在数学中,指一个向量空间,并在其上定义了一个范数(norm),用来度量向量的“长度/大小”。(常见于线性代数与泛函分析;相关概念还包括度量空间与巴拿赫空间。)

发音 Pronunciation (IPA)

/nrmd spes/

例句 Examples

A normed space is a vector space equipped with a norm.
赋范空间是一个配备了范数的向量空间。

In a normed space, convergence of a sequence is defined by the norm, which is fundamental for studying continuous and bounded linear operators.
在赋范空间中,序列的收敛由范数来定义,这对研究连续与有界线性算子非常基础。

词源 Etymology

normed 来自 norm(范数/标准) + -ed(形容词后缀,表示“被……所赋予/具有……的”),因此 normed 表示“带有范数的”;space 在数学语境中常指“空间/集合结构”。合起来 normed space 即“赋予范数的空间(向量空间)”。

相关词 Related Words

文学与著作中的用例 Literary & Notable Works

  • Walter Rudin,《Functional Analysis
  • Erwin Kreyszig,《Introductory Functional Analysis with Applications
  • John B. Conway,《A Course in Functional Analysis
  • Michael Reed & Barry Simon,《Methods of Modern Mathematical Physics, Vol. I: Functional Analysis
  • Nelson Dunford & Jacob T. Schwartz,《Linear Operators
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