different between idempotent vs projection

English

Etymology

Latin roots, idem (“same”) +? potent (“having power”) – literally, “having the same power”.

Coined 1870 by American mathematician Benjamin Peirce in context of algebra.

Pronunciation

• (US) IPA^(key): /a?.d?m?po?.t?nt/, /?.d?m?po?.t?nt/

Adjective

idempotent (not comparable)

1. (mathematics, computing) Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.

   A projection operator is idempotent.

2. (mathematics) Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.

   Every finite semigroup has an idempotent element.

   Every group has a unique idempotent element: namely, its identity element.

3. (mathematics) Said of a binary operation: such that all of the distinct elements it can operate on are idempotent (in the sense given just above).

   Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself.

4. (mathematics) Said of an algebraic structure: having an idempotent operation (in the sense above).

Usage notes

See the Usage notes section of nullipotent.

Coordinate terms

• nilpotent
• nullipotent

Related terms

• idempotence
• nilpotent
• nullipotent
• unipotent

Translations

Noun

idempotent (plural idempotents)

1. (mathematics) An idempotent element.
2. (mathematics) An idempotent structure.

References

• “idempotent” at FOLDOC

German

Pronunciation

Adjective

idempotent

1. idempotent

Swedish

Adjective

idempotent

1. idempotent

Turkish

Adjective

idempotent

1. idempotent

English

Etymology

From either the Middle French projection or its etymon, the Classical Latin pr?iecti? (stem: pr?iecti?n-), from pr?ici?. Compare the Modern French projection, the German Projektion, and the Italian proiezione.

Pronunciation

• IPA^(key): /p???d??k??n/
• Rhymes: -?k??n

Noun

projection (countable and uncountable, plural projections)

1. Something which projects, protrudes, juts out, sticks out, or stands out.

   The face of the cliff had many projections that were big enough for birds to nest on.

2. The action of projecting or throwing or propelling something.
   1. (archaic) The throwing of materials into a crucible, hence the transmutation of metals.
3. (archaic) The crisis or decisive point of any process, especially a culinary process.
4. The display of an image by devices such as movie projector, video projector, overhead projector or slide projector.
5. A forecast or prognosis obtained by extrapolation
6. (psychology) A belief or assumption that others have similar thoughts and experiences as oneself
7. (photography) The image that a translucent object casts onto another object.
8. (cartography) Any of several systems of intersecting lines that allow the curved surface of the earth to be represented on a flat surface. The set of mathematics used to calculate coordinate positions.
9. (geometry) An image of an object on a surface of fewer dimensions.
10. (linear algebra) An idempotent linear transformation which maps vectors from a vector space onto a subspace.
11. (mathematics) A transformation which extracts a fragment of a mathematical object.
12. (category theory) A morphism from a categorical product to one of its (two) components.

Synonyms

• (something which sticks out): protuberance

Derived terms

Related terms

• project

Translations

Further reading

• projection on Wikipedia.Wikipedia

French

Pronunciation

Noun

projection f (plural projections)

1. projection
2. screening (of a film)

Interlingua

Noun

projection (plural projectiones)

1. projection