different between mathematical vs automorphism

English

Etymology

mathematics +? -al

Pronunciation

• (Received Pronunciation) IPA^(key): /?mæ???mæt?k?l/
• (General American, weak vowel distinction) IPA^(key): /?mæ???mæt?k?l/
  • (weak vowel merger) IPA^(key): /?mæ???mæt?k?l/

Adjective

mathematical (comparative more mathematical, superlative most mathematical)

1. Of, or relating to mathematics
   • 1897, Thomas Hardy, The Well-Beloved

     […] he looked up the uninteresting left road to the fortifications. It was new, long, white, regular, tapering to a vanishing point, like a lesson in perspective. […] Smaller and smaller she waned up the rigid mathematical road, still gazing at the soldier aloft, as Pierston gazed at her.

   • Although Galileo had designed a pendulum clock, he never actually constructed one. The first pendulum clock was constructed by the Dutch physicist Christian Huygens (1629–1695) in 1657. He also developed the mathematical theory of the pendulum. Newton also studied the motion of a pendulum and experimented with pendulums made of different materials and of different lengths.
2. Possible but highly improbable

Translations

Anagrams

• metathalamic

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)