Norm

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See: Social Norm, Mathematical Norm (vector norm, matrix norm), Substantive Norm, NORM, Norm (Philosophy), Basic Norm, Peremptory Norm, Norm (Artificial Intelligence), Naturally Occurring Radioactive Material, Operator Norm.



References

2020

2015

  • https://en.wiktionary.org/wiki/norm#Noun
    1. That which is regarded as normal or typical.
      Unemployment is the norm in this part of the country.
    2. A rule that is enforced by members of a community.
      Not eating your children is just one of those societal norms.
    3. (Philosophy, Computer Science) A sentence with non-descriptive meaning, such as a command, permission · or prohibition.
    4. (Mathematics) A function, generally denoted [math]\displaystyle{ v\mapsto\left|v\right| }[/math] or [math]\displaystyle{ v\mapsto\left\|v\right\| }[/math], that maps vectors to non-negative scalars and has the following properties:
      1. if [math]\displaystyle{ v\ne0 }[/math] then [math]\displaystyle{ \left\|v\right\|\ne0 }[/math];
      2. given a scalar [math]\displaystyle{ k }[/math], [math]\displaystyle{ \left\|kv\right\|=\left|k\right|\cdot\left\|v\right\| }[/math], where [math]\displaystyle{ \left|k\right| }[/math] is the absolute value of [math]\displaystyle{ k }[/math];
      3. given two vectors [math]\displaystyle{ v,w }[/math], [math]\displaystyle{ \left\|v+w\right\|\le\left\|v\right\|+\left\|w\right\| }[/math] (the triangle inequality).
    5. (Chess) A high level of performance in a chess tournament, several of which are required for a player to receive a title.

2023