(adsbygoogle = window.adsbygoogle || []).push({}); norm of a function ||f|| & the "root mean square" of a function.

How do I explain the connection between the norm of a function ||f|| & the "root mean square" of a function. You may like to consider as an example C[0,[tex]\pi[/tex]], the inner product space of continuous functions on the interval [0,[tex]\pi[/tex]] with the inner product

(f,g) = [tex]\int_0^\pi[/tex] f(x)g(x) dx.

Let f(x) = sin(x). How do I find ||f||. Also find "root mean square" of f. What do you notice?

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# Norm of a function ||f|| & the root mean square of a function.

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