noun
- 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.