1. a mathematical transformation of a structure onto itself that preserves the structure’s properties
Usage: mathematics

Examples

• The rotation of a square by 90 degrees is an automorphism of the square.
• In group theory, an automorphism maps each element to another element while preserving the group operation.
• The identity function is always an automorphism of any mathematical structure.
• Mathematicians study automorphisms to understand the symmetries of algebraic structures.
• The set of all automorphisms of a group forms another group called the automorphism group.
• Complex conjugation is an automorphism of the field of complex numbers.