norm
verbEtymology Back-formation from normed.
1
Mathematical analysis, Mathematics, Sciences To endow (a vector space, etc.) with a norm.
- Derived terms
- norming
norm
nounUK /nɔːm/ · CA, US /noɹm/
Etymology From Latin norma (“a carpenter's square, a rule, a pattern, a precept”). Doublet of norma.
9 senses
- 1That which is normal or typical.
- 2A rule that is imposed by regulations and/or socially…
- 3A sentence with non-descriptive meaning, such as a…
- 4if v ne 0 then ‖v‖ ne 0;
- 5given a scalar k, ‖kv‖=|k|·‖v‖, where |k| is the…
- 6given two vectors v,w, ‖v+w‖<‖v‖+‖w‖ (the triangle inequality).
- 7Any of several generalizations of the above: a field…
- 8An element of the image of some (generalized) norm, the…
- 9A high level of performance in a chess tournament…
1
That which is normal or typical.
- Unemployment is the norm in this part of the country.
- […] the world needs a constitutional moment that will generate new institutions and actuate a new norm.2008, Dennis Patterson, Ari Afilalo, The New Global Trading Order: The Evolving State and the Future of Trade:
3 more examples
- "This shocking report proves once again that we urgently need a radical shake-up of hospital care," said Jeremy Hughes, chief executive of the Alzheimer's Society. "Given that people with dementia occupy a quarter of hospital beds and that many leave in worse health than when they were admitted, it is unacceptable that training in dementia care is not the norm."2011 December 16, Denis Campbell, “Hospital staff 'lack skills to cope with dementia patients'”, in The Guardian, archived from the original on 31 May 2022:
- Projects such as the King's Cross refurbishment, Waterloo blockade, Scottish electrification and the Borders show that the industry can do wonderful work - but that must become the norm, not the exception.2019 December 18, Richard Clinnick, “Railway's 2020 vision”, in Rail, page 3:
- For most people, this sacrifice is made easily and instinctively. Not so for otroverts, who are neither willing nor able to passively adopt the social scripts that others do. To the otrovert, who is constantly engaged with the choices and consequences of their individual life, social norms follow a circular logic: […]2025 June 19, Rami Kaminski, ““Otroverts” and why nonconformists often see what others can’t”, in Big Think, archived from the original on 15 Jul 2025:
2
A rule that is imposed by regulations and/or socially enforced by members of a community.
- Not eating your children is just one of those societal norms.
- Peer pressure helps explain why people in Europe weigh less than Americans: They follow different social norms, like eating only at mealtimes instead of snacking throughout the day.2011, Roy F. Baumeister, John Tierney, Willpower, →ISBN, page 230:
3
Computer, Computing, Engineering, Human sciences, Mathematics, Natural sciences, Philosophy, Physical sciences, Science, Sciences A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
› A function which satisfies a particular set…
4
Mathematics, Sciences if v ne 0 then ‖v‖ ne 0;
5
Mathematics, Sciences given a scalar k, ‖kv‖=|k|·‖v‖, where |k| is the absolute value of k;
6
Mathematics, Sciences given two vectors v,w, ‖v+w‖<‖v‖+‖w‖ (the triangle inequality).
7
Mathematics, Sciences Any of several generalizations of the above: a field norm, ideal norm, etc.
8
Algebra, Mathematics, Sciences 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.
- A quaternion algebra (a,b) over ksplits if and only if b is a norm from the field extension k(#92;sqrt#123;a#125;)#47;k, i.e. if and only if there is some x in k(#92;sqrt#123;a#125;) which has field norm exactly equal to b.
9
Board games, Chess, Games A high level of performance in a chess tournament, several of which are required for a player to receive a title.
- Derived terms
116 terms
1-norm, 2-norm, absolute norm, adnorm, age norm, Banach norm, basic norm, Bombieri norm, C*-cross norm, Chebyshev norm, complex norm, conorm, copynorm, Cr-norm, cross norm, Dedekind-Hasse norm, dual norm, ethical norm, Euclidean matrix norm, Euclidean norm, Euclidean vector norm, exonorm, extended norm, field norm, flat norm, four-vector norm, Frobenius matrix norm, Frobenius norm, Frobenius norm function, Gowers norm, grandmaster norm, graph norm, Hardy norm, Hilbert-Schmidt norm, ideological norm, induced norm, infinity-norm, integral flat norm, l1 norm, l2 norm, L-infinity norm, male as norm, mass norm, matrix F-norm, matrix norm, matrix p-norm, maximum absolute row column norm, maximum absolute row sum norm, maximum norm, metanorm, metric induced by a norm, minimum norm property, Minkowski norm, Mistralian norm, moral norm, multinorm, natural norm, normable, normation, normcore, normed, norm form, norm function, normic form, normie, normless, normlessness, norm of an ideal, norm of communism, norm of disinterestedness, norm of organized skepticism, norm of reaction, norm of reciprocity, norm of universalism, norm-referenced, norm-referencing, norm-residue, norm resolvent convergence, norm theorem, normwise, nuclear norm, operator norm, p-adic norm, peremptory norm, p-norm, polynomial bar norm, polynomial bracket norm, polynomial norm, pseudonorm, quasinorm, quaternion norm, reduced norm, regular norm, relative norm, renorm, seminorm, semi-norm, sexual norm, social norm, spectral norm, spinorial norm, spinor norm, statistical norm, subordinate norm, sup-norm, sup norm, supremum norm, t-norm, T-norm, t-norm fuzzy logic, tobacco-free social norm, trace norm, two-norm, uniform norm, vector norm, vector p-norm