1. A function or mapping from a mathematical structure to itself that preserves the structure's operations.
Usage: mathematics; formal

Examples

• In group theory, an endomorphism is a homomorphism from a group to itself.
• The identity function is a trivial example of an endomorphism on any set.
• Endomorphisms of a vector space form a ring under composition and addition.
• The study of endomorphisms helps mathematicians understand the internal structure of algebraic objects.
• An automorphism is a special case of an endomorphism that is also bijective.