Norm (mathematics): Difference between revisions
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imported>Hendra I. Nurdin (Stub for norm) |
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Revision as of 07:25, 26 September 2007
In mathematics, a norm is a function on a vector space that generalizes to vector spaces the notion of the distance from a point of a Euclidean space to the origin.
Formal definition of norm
Let X be a vector space. Then a norm on X is any function having the following three properties:
- for all (positivity)
- if and only if x=0
- for all (triangular inequality)
A norm on X can immediately obtained from any metric on X as .