Normed vector space

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In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V {\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R {\displaystyle \mathbb {R} } or to C {\displaystyle \mathbb {C} } , then a norm on V {\displaystyle V} is a map V → R {\displaystyle V\to \mathbb {R} } , typically denoted by ‖ ⋅ ‖ {\displaystyle \lVert \cdot \rVert...

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