what is normed vector space
A normed vector space is a pair (V, âÂ·â) where V is a vector space and âÂ·â a norm on V.A seminormed vector space is a pair (V, p) where V is a vector space and p a seminorm on V.imilarly, for any semi-normed vector space we can define the distance between two vectors u and v as â u â v â. This turns the seminormed space into a pseudometric space (notice this is weaker than a metric) and allows the definition of notions such as continuity and convergence.
A vector space on which a norm is defined is then called a normed vector space. Normed vector spaces are central to the study of linear algebra and functional analysis.imilarly, for any semi-normed vector space we can define the distance between two vectors u and v as â u â v â. This turns the seminormed space into a pseudometric space (notice this is weaker than a metric) and allows the definition of notions such as continuity and convergence.