Normed Vector Spaces
By definition, all Euclidean vectors have a magnitude (see above). However, the notion of magnitude cannot be applied to all kinds of vectors.
A function that maps objects to their magnitudes is called a norm. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. In high mathematics, not all vector spaces are normed.
Read more about this topic: Magnitude (mathematics)
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