What is the meaning of Norm?

That which is normal or typical.

A rule that is imposed by regulations and/or socially enforced by members of a community.

A sentence with non-descriptive meaning, such as a command, permission, or prohibition.

A function which satisfies a particular set of formal conditions, created to generalize the notion of the length of a vector. Formally, a real-valued function on a vector space, generally denoted ${\displaystyle v\mapsto \left|v\right|}$ or ${\displaystyle v\mapsto \left\|v\right\|}$, that satisfies 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).

if ${\displaystyle v\neq 0}$ then ${\displaystyle \left\|v\right\|\neq 0}$;

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 ${\displaystyle k}$;

given two vectors ${\displaystyle v,w}$, ${\displaystyle \left\|v+w\right\|\leq \left\|v\right\|+\left\|w\right\|}$ (the triangle inequality).

Any of several generalizations of the above: a field norm, ideal norm, etc.

1. 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.

   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 high level of performance in a chess tournament, several of which are required for a player to receive a title.

   To endow (a vector space, etc.) with a norm.

   norm; standard

   a norm, standard

   norm (that which is normal)

   A norm (that which is normal).

   lawn

   meadow

   norm (that which is normal)

   norm (in analysis)

   Source: wiktionary.org