Sanakirja.org

Määritelmät

Substantiivi

1. That which is normal or typical.
2. A rule that is imposed by regulations and/or socially 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 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 v\mapsto\left|v\right| or v\mapsto\left\|v\right\|, that satisfies the following properties:
5. if ${\displaystyle v\neq 0}$ then \left\|v\right\|\ne0;
6. given a scalar ${\displaystyle k}$, \left\|kv\right\|=\left|k\right|·\left\|v\right\|, where \left|k\right| is the absolute value of ${\displaystyle k}$;
7. given two vectors ${\displaystyle v,w}$, \left\|v+w\right\|\le\left\|v\right\|+\left\|w\right\| (the triangle inequality).
8. (mathematics) Any of several generalizations of the above: a field norm, ideal norm, etc.
9. (algebra) 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.
10. (chess) A high level of performance in a chess tournament, several of which are required for a player to receive a title.

Verbi

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