Automorphism

Part of speech: noun

Definitions

1. A specific type of mapping in mathematics refers to a transformation that preserves both the structure and properties of an object while returning the object to its original form
2. In the realm of mathematics, there exists a function that operates on a given structure and yields the same entity while ensuring the preservation of all defining features
3. A mathematical function showcases an internal symmetry by transforming an object in such a way that both its structure and properties remain intact while yielding the original object

Etymology: "Automorphism" is a plain technical coinage, built from two Greek-derived pieces. The first, "auto-", comes from Ancient Greek "autós", meaning "self" or "same", a form that goes back to a Proto-Indo-European root combining an old particle with a demonstrative pronoun. The second, "morphism", is a mathematical term for a structure-preserving map between two objects, and it carries the Greek "morphḗ", meaning "form" or "shape". Put together, the word describes a map from a mathematical structure to itself: the "self-form" of the object, in which the shape is kept intact while the individual elements may be rearranged. Its meaning follows directly from its parts, with no shift in sense along the way.

Synonyms: self-mapping, self-transforming