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)
Famous quotes containing the word spaces:
“When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
—Blaise Pascal (1623–1662)