## NORM

### Norm

In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space, other than the zero vector . A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors .

The above text is a snippet from Wikipedia: Norm (mathematics)

### N or M?

N or M? is a work of detective fiction by Agatha Christie first published in the US by Dodd, Mead and Company in 1941 and in the UK by the Collins Crime Club in November of the same year. The US edition retailed \$2.00 and the UK edition at seven shillings and sixpence .

The above text is a snippet from Wikipedia: N or M?

### 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. A sentence with non-descriptive meaning, such as a command, permission or prohibition.
4. A function, generally denoted $v\mapsto\left|v\right|$ or $v\mapsto\left\|v\right\|$, that maps vectors to non-negative scalars and has the following properties:
1. if $v\ne0$ then $\left\|v\right\|\ne0$;
2. given a scalar $k$, $\left\|kv\right\|=\left|k\right|\cdot\left\|v\right\|$, where $\left|k\right|$ is the absolute value of $k$;
3. given two vectors $v,w$, $\left\|v+w\right\|\le\left\|v\right\|+\left\|w\right\|$ (the triangle inequality).
5. A high level of performance in a chess tournament, several of which are required for a player to receive a title.

#### Verb

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

The above text is a snippet from Wiktionary: norm