Normed Vector Space
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High Quality Content by WIKIPEDIA articles! 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 R^n. A seminormed vector space is a pair (V,p) where V is a vector space and p a seminorm on V. A normed vector space is a pair (V, · ) where V is a vector space and · a norm on V. We often omit p or · and just write V for a space if it is clear from the context what (semi) norm we are using.

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High Quality Content by WIKIPEDIA articles! 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 R^n. A seminormed vector space is a pair (V,p) where V is a vector space and p a seminorm on V. A normed vector space is a pair (V, · ) where V is a vector space and · a norm on V. We often omit p or · and just write V for a space if it is clear from the context what (semi) norm we are using.