V2EX endomorphism

Endomorphism

定义 Definition

endomorphism(名词):(数学)自同态,指从某个代数结构(如群、环、向量空间、范畴中的对象)映射到它自身并保持其结构的函数/态射。常见于抽象代数、线性代数与范畴论。(也有更广义的“内部映射”用法,但数学义最常见。)

发音 Pronunciation

/endomrfzm/

例句 Examples

An endomorphism maps a vector space to itself.
自同态把一个向量空间映射到它自身。

In group theory, an endomorphism that is bijective is called an automorphism, and the set of all endomorphisms forms a monoid under composition.
在群论中,若一个自同态是双射,则称为自同构;所有自同态在复合运算下构成一个幺半群。

词源 Etymology

来自希腊语词根:endo- 表示“内部、在……之内”,**-morphism** 源于 morphē(形式、形态)并在数学中引申为“保持结构的映射/变换”。合起来即“作用在内部(自身)上的结构保持映射”。

相关词 Related Words

文献与作品 Literary Works

  • Algebra Serge Lang(朗)
  • Abstract Algebra David S. Dummit & Richard M. Foote
  • Categories for the Working Mathematician Saunders Mac Lane(麦克莱恩)
  • Algebra(Graduate Texts in Mathematics) Michael Artin(阿廷)
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