different between automorphism vs endomorphism

English

Etymology

auto- +? morphism

Noun

automorphism (plural automorphisms)

1. (algebra) An isomorphism of a mathematical object or system of objects onto itself.
2. The ascription to others of one's own characteristics.

Usage notes

• (algebra):
  • An automorphism is characterised by the structure it preserves, which is usually specified as an object type. Thus one may speak of a group automorphism or ring automorphism.
  • The identity mapping is sometimes called the trivial automorphism; any other automorphism may then be called a nontrivial automorphism.

Synonyms

• (isomorphism of a mathematical object or system of objects onto itself): self-map
• (ascription to others of one's own characteristics): projection

Hypernyms

• (algebra): isomorphism, endomorphism

Hyponyms

• (algebra): inner automorphism, outer automorphism, Möbius transformation

Derived terms

• automorphism group

Translations

See also

• self-map

Further reading

• Automorphism in the Encyclopædia Britannica (11th edition, 1911)

English

Etymology

endo- +? -morphism

Noun

endomorphism (plural endomorphisms)

1. (geology) The assimilation of surrounding rock by an intrusive igneous rock
2. (mathematics) A homomorphism that maps a system to itself

Hyponyms

• (mathematics): automorphism

Translations

Further reading

• endomorphism on Wikipedia.Wikipedia