normed vector space

In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. It turns out that the following properties of "vector length" are the crucial ones.The zero vector, 0, has zero length; every other vector has a positive length.Multiplying a vector by a positive number changes its length without changing its direction. See unit vector.The triangle inequality holds. That is, taking norms as distances, the distance from A through B to C is never shorter than going directly from A to C, or the shortest distance between any two points is a straight line.
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