All continuous functions on closed interval [a, b] form a vector space. The functions in this space are the vectors. However what is the physical significance of the norm of a vector in this space? For example if we found the norm of a function is 1/3 what does this signify? Does it dependent on the inner product used to define the norm?(adsbygoogle = window.adsbygoogle || []).push({});

Say if the inner product is the integral over [a, b] does this mean that the norm is related to the area?

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# Norms of a general vector space

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