Number & MeasureGreek → English
Endomorphism
/ˌɛndoʊˈmɔːrfɪzəm/noun
A structure-preserving map from a mathematical object to itself.
The Greek roots
ἔνδον
éndon
within
μορφή
morphḗ
form, shape
Literally: “forming within”
The story of the word
Algebra needed a name for a map that stays at home, and ἔνδον supplied it: the source and the target are the same object. Every square matrix is an endomorphism of a vector space, which is why the set of them is closed under multiplication as well as addition. The same prefix in a different field gave William Sheldon his endomorph in the 1940s, a body-type scheme named after embryonic germ layers and now discarded by serious physiology.
- How it travelled
- Ancient Greek → mathematical coinage → English
- First recorded
- 20th century
Same family
endoscopeendocrinemorphologyisomorphism
In a sentence
Differentiation is an endomorphism of the space of polynomials.
The endomorphisms of an abelian group form a ring under composition.