An isomorphism of a mathematical object with itself—so a one-to-one correspondence from a set onto itself, preserving any further structure (usually algebraic) that is present. For example, complex conjugation is an automorphism of ℂ as a group or field or real vector space but not as a complex vector space, as it does not respect scalar multiplication. The set of automorphisms of an object X, under composition, then form the automorphism group denoted Aut(X).