# norm

Pronunciation: say "NORM" US /nɔɹm/, UK /nɔːm/

## Noun

1. A rule imposed by regulations, or enforced socially by the members of a community.
   - Simple: A rule that people in a group are expected to follow and keep each other to.
   - _Punctuality quickly became a firm norm within the new management team._
   - _Communities enforce their norms through quiet pressure rather than formal punishment._
2. What is normal or typical; the usual state of things.
   - Simple: The usual or expected thing that most people are used to.
   - _Remote meetings rapidly became the norm during the pandemic._
   - _In many offices, working from home a few days a week is now the norm._
3. In mathematics, a real-valued function on a vector space, usually written ‖v‖ or |v|, that meets a set of formal conditions designed to generalize a vector's length.
   - Simple: In math, a function that gives every vector a number acting like its length, following certain fixed rules.
   - _Every inner product on a vector space induces a norm, but not every norm comes from an inner product._
   - _Many machine-learning models add a penalty based on the norm of the weight vector to keep the weights small._

## Other meanings

- (noun) A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
- (noun) Any of several generalizations of the above: a field norm, ideal norm, etc.
- (noun) A high level of performance in a chess tournament, several of which are required for a player to receive a title.
- (noun) An element of the image of some (generalized) norm, the element then said to be from the norm in question, or from the structure which gave rise to the norm.
- (verb) To endow (a vector space, etc.) with a norm.

## Origin

From Latin norma ("a carpenter's square, a rule, a pattern, a precept"). It is a doublet of norma.

Source: DictionaryAI, https://dictionaryai.com/define/norm (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).