Vs metric:
- a norm is the size of one element. A metric is the distance between two elements.
- a norm is only defined on a vector space. A metric could be defined on something that is not a vector space. Most basic examples however are also vector spaces.
In mathematics, particularly in linear algebra and functional analysis, a **norm** is a function that assigns a non-negative length or size to vectors in a vector space. Norms provide a means to measure distance and size in various mathematical contexts.
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