Norm (mathematics), Norm
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Norm, the Norm or NORM may refer to:


In academic disciplines

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Normativity Normativity is the phenomenon in human societies of designating some actions or outcomes as good, desirable, or permissible, and others as bad, undesirable, or impermissible. A Norm (philosophy), norm in this sense means a standard for evaluatin ...
, phenomenon of designating things as good or bad * Norm (geology), an estimate of the idealised mineral content of a rock *
Norm (philosophy) Norms are concepts ( sentences) of practical import, oriented to affecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply "ought-to" (or "may", "may not") types of statements and asse ...
, a standard in normative ethics that is prescriptive rather than a descriptive or explanatory abstraction *
Social norm A social norm is a shared standard of acceptance, acceptable behavior by a group. Social norms can both be informal understandings that govern the behavior of members of a society, as well as be codified into wikt:rule, rules and laws. Social norma ...
, shared standards of acceptable behavior by groups *
Basic norm () is a concept in the '' Pure Theory of Law'' created by Hans Kelsen, a jurist and legal philosopher. Kelsen used this word to denote the basic norm, order, or rule that forms an underlying basis for a legal system. The theory is based on a ...
, a jurisprudence concept by Kelsen *
Peremptory norm A peremptory norm (also called ) is a fundamental principle of international law that is accepted by the international community of states as a norm from which no derogation is permitted. There is no universal agreement regarding precisely w ...
, a fundamental principle of international law *
Norm (artificial intelligence) Norms can be considered from different perspectives in artificial intelligence to create computers and computer software that are capable of intelligent behaviour. In artificial intelligence and law, legal norms are considered in computational t ...
, a set of statements used to regulate artificial intelligence software * Norm, a statistical concept in
psychometrics Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally covers specialized fields within psychology and education devoted to testing, measurement, assessment, and rela ...
representing the aggregate responses of a standardized and representative group * NORM,
naturally occurring radioactive material Naturally occurring radioactive materials (NORM) and technologically enhanced naturally occurring radioactive materials (TENORM) consist of materials, usually industrial wastes or by-products enriched with radioactive materials, radioactive elem ...
s * NORM (non-mobile older rural males), an acronym in dialect studies coined by Chambers and Trudgill (1980) for a group to which speakers frequently refer


In mathematics

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Norm (mathematics) In mathematics, a norm is a function (mathematics), function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the Origin (mathematics), origin: it Equivariant map, commutes w ...
, a map that assigns a length or size to a mathematical object, including: **
Vector norm In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and zero ...
, a map that assigns a length or size to any vector in a vector space **
Matrix norm In the field of mathematics, norms are defined for elements within a vector space. Specifically, when the vector space comprises matrices, such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also ...
, a map that assigns a length or size to a matrix **
Operator norm In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its . Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Inform ...
, a map that assigns a length or size to any operator in a function space ** Norm (abelian group), a map that assigns a length or size to any element of an abelian group *
Field norm In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield. Formal definition Let ''K'' be a field and ''L'' a finite extension (and hence an algebraic extension) o ...
a map in algebraic number theory and Galois theory that generalizes the usual distance norm *
Ideal norm In commutative algebra, the norm of an ideal is a generalization of a norm of an element in the field extension. It is particularly important in number theory since it measures the size of an ideal of a complicated number ring in terms of an ide ...
, the ideal-theoretic generalization of the field norm *
Norm (group) In mathematics, in the field of group theory, the norm of a group is the intersection of the normalizers of all its subgroup In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form ...
, a certain subgroup of a group * Norm map, a map from a pointset into the ordinals inducing a
prewellordering In set theory, a prewellordering on a set X is a preorder \leq on X (a transitive and reflexive relation on X) that is strongly connected (meaning that any two points are comparable) and well-founded in the sense that the induced relation x < y< ...
*
Norm group In number theory, a norm group is a group of the form N_(L^\times) where L/K is a finite abelian extension of nonarchimedean local fields, and N_ is the field norm. One of the main theorems in local class field theory states that the norm groups in ...
, a group in class field theory that is the image of the multiplicative group of a field * Norm function, a term in the study of
Euclidean domain In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of Euclidean division of integers. Th ...
s, sometimes used in place of "Euclidean function" *
Norm (descriptive set theory) In set theory, a prewellordering on a set X is a preorder \leq on X (a transitive and reflexive relation on X) that is strongly connected (meaning that any two points are comparable) and well-founded in the sense that the induced relation x < y< ...
, a map from a set into the ordinals


People

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Norm (given name) Norm is a masculine given name, most often a short form (hypocorism) of Norman. People named Norm include: * Norm Abram (born 1949), carpenter on the television show ''This Old House'' * Norm Cash (1933–1986), American baseball player * Norm Cho ...
*
Norm Macdonald Norman Gene MacdonaldThe capitalization of Norm Macdonald's surname has been inconsistently reported in publications such as ''TV Guide''. Books that discuss him, such as ''Shales'' (2003) and Crawford' (2000), as well as other sources such as ...
, a Canadian stand-up comedian


Arts and entertainment

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Norm Peterson Hilary Norman Peterson is a regular fictional character on the American television show ''Cheers''. The character was portrayed by actor George Wendt and is named Hilary after his paternal grandfather. Norm appeared in all 275 episodes of ' ...
, a character in the sitcom ''Cheers'' and its spin-off ''Frasier'' * Norm, a recurring character in ''Phineas and Ferb'' * ''The Norm'' (comic strip), syndicated by Michael Jantze * ''The Norm'' (radio), a former CBC radio show * The Norm, a character in the 1989 film ''
Spirits of the Air, Gremlins of the Clouds ''Spirits of the Air, Gremlins of the Clouds'' is a 1989 Australian independent science fiction adventure film directed, produced and written by Alex Proyas, who was making his first feature debut. Set in a post-apocalyptic world in which two si ...
'' * Norm, the main character in the ''
Norm of the North ''Norm of the North'' is a 2016 animated comedy film directed by Trevor Wall in his directorial debut, and written by Daniel R. Altiere, Steven M. Altiere, and Malcolm T. Goldman. The film features the voices of Rob Schneider, Heather Graham ...
'' films *
Norm (album) ''Norm'' is the ninth studio album by Canadian musician Andy Shauf. It was released on February 10, 2023, by Anti-. Background After releasing concept albums such as 2016's ''The Party'', 2020's '' The Neon Skyline'', and 2021's ''Wilds'', ...
, a 2023 album by Andy Shauf


Other uses

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National Organization of Russian Muslims The National Organization of Russian Muslims (NORM) is an organization of the Russian Muslims, founded in 2004 on the basis of Russian Muslim communities of Moscow (Banu Zulkarnain), Yoshkar-Ola (Tsaryovokokshaysk Community of Russian Muslims), ...
, a religious organization based in Russia *
Norm (chess) A norm in chess is a high level of performance in a chess tournament. The level of performance is typically measured in tournament performance rating above a certain threshold (for instance, 2600 for GM norm), and there is a requirement on the leve ...
, a chess result required to qualify for an official title *
NORM Norm, the Norm or NORM may refer to: In academic disciplines * Normativity, phenomenon of designating things as good or bad * Norm (geology), an estimate of the idealised mineral content of a rock * Norm (philosophy), a standard in normative e ...
(NACK-Oriented Reliable Multicast), a
transport protocol Transport (in British English) or transportation (in American English) is the intentional movement of humans, animals, and goods from one location to another. Modes of transport include air, land ( rail and road), water, cable, pipelines, a ...
* Norm, a character from the Australian government physical fitness program and advertising campaign " Life. Be in it." * Norms Restaurants, a chain of restaurants in Southern California


See also

* ''
The Norm Show ''The Norm Show'' is an American television sitcom that ran on ABC from March 24, 1999, to April 6, 2001. Starting in September 1999, the show's title was shortened to ''Norm''. The series starred Norm Macdonald, who created the series with B ...
'', a television series featuring Norm Macdonald * Norman (disambiguation) *
Normal (disambiguation) Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...
* Norma (disambiguation) *
Technical standard A technical standard is an established Social norm, norm or requirement for a repeatable technical task which is applied to a common and repeated use of rules, conditions, guidelines or characteristics for products or related processes and producti ...
{{disambig eo:Normo