automorphism

Noun

automorphism (countable and uncountable, plural automorphisms)

1. An isomorphism of a mathematical object or system of objects onto itself.
   • Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because...1971, Norman Biggs, Finite Groups of Automorphisms: Course Given at the University of Southampton, Cambridge University Press, page 25
   • In mathematics, automorphisms of algebraic structures play an important role. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure.2005, Maninda Agrawal, Nitin Saxena, “Automorpisms of Finite Rings and Applications to Complexity of Problems”, in Volker Diekert, Bruno Durand, editors, STACS 2005: 22nd Annual Symposium on...

   Synonyms:

   self-map

2. The ascription to others of one's own characteristics or of one's own perceived characteristics.
   • Sensation for us is a complex of sensations plus perceptions and other cognitive and emotional elements which lie beyond early mind, but which by an inevitable automorphism we interpret into early forms. This automorphism with the child is complete, and is never perfectly effaced even in the most...1895 Hiram M. Stanley: Studies in the Evolutionary Psychology of Feeling. MacMillan

   Synonyms:

   heautomorphism, projection