norm

1. (philosophy, computer science) A sentence with non-descriptive meaning, such as a command, permission, or prohibition.

2. (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↦|v| or v↦‖v‖, that satisfies the following properties:

3. (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↦|v| or v↦‖v‖, that satisfies the following properties:

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↦|v| or v↦‖v‖, that satisfies the following properties:

5. (mathematics) Any of several generalizations of the above: a field norm, ideal norm, etc.

6. (mathematics) Any of several generalizations of the above: a field norm, ideal norm, etc.Examples: "A quaternion algebra (a,b) over ksplits if and only if b is a norm from the field extension k(#92;sqrt#123;a#125;)#47;k, i.e. if and only if there is some x in k(#92;sqrt#123;a#125;) which has field norm exactly equal to b."