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Definition norm

Etymology 1

From French norme, from Old French, from Latin norma (“a carpenter's square, a rule, a pattern, a precept”).

Noun

norm (plural norms)

1. That which is normal or typical.
2. A rule that is enforced by members of a community.
3. (philosophy, computer science) A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
4. (mathematics) A function, generally denoted ${\displaystyle v\mapsto \left|v\right|}$ or ${\displaystyle v\mapsto \left\|v\right\|}$, that maps vectors to non-negative scalars and has the following properties:
   1. if ${\displaystyle v\neq 0}$ then ${\displaystyle \left\|v\right\|\neq 0}$;
   2. given a scalar ${\displaystyle k}$, ${\displaystyle \left\|kv\right\|=\left|k\right|\cdot \left\|v\right\|}$, where ${\displaystyle \left|k\right|}$ is the absolute value of ${\displaystyle k}$;
   3. given two vectors ${\displaystyle v,w}$, ${\displaystyle \left\|v+w\right\|\leq \left\|v\right\|+\left\|w\right\|}$ (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.