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from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. An isomorphism of a mathematical object or system of objects onto itself.

from the GNU version of the Collaborative International Dictionary of English

  • n. Automorphic characterization.

from The Century Dictionary and Cyclopedia

  • n. The ascription of one's own characteristics to another, or the habit of judging others or explaining their acts by means of analogies furnished by the knowledge of one's self.
  • n. In mathematics, the property of remaining unchanged by all the substitutions of any group of linear transformations.
  • n. Anthropomorphism; the conception of the lower animals by analogy with man.


auto- +‎ morphism (Wiktionary)


  • This has as its automorphism groups F_4 whose root space is a minimal tessellation in 4 dimensions and G_2.

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  • But since Ï is an automorphism, it also preserves function application, so that Ï (f (U)) = Ïf (Ï (U)).

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  • Sym (V) is also a model of set theory with set of atoms A, and Ï induces an automorphism of Sym (V).

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  • If is a model of Z (Zermelo set theory) with an external automorphism σ and an ordinal κ such that κ σ (κ), then

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  • If the space is a so-called metric space, it is usually expected that the underlying automorphism shall at least be isometric, meaning that the transformations preserve the distance between any pair of points.


  • Obviously the homogeneity of a space is the more interesting if the underlying group of automorphism is more important.


  • In general, an automorphism of a space, any space, is an invertible transformation of the entire space into itself, and such a transformation is nothing other than a rearrangement of the totality of the points of the space from their given ordering into any other.


  • Inasmuch as a mirror reflection of the space is a transformation of the entire space into itself it is called an automorphism.


  • If such a group is given and held fast, then a figure in space is called symmetric if each automorphism of the group leaves it unchanged.


  • Moore determinant: A determinant defined over a finite field which has successive powers of the Frobenius automorphism applied to the first column.

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