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Inner product of functions

  1. Apr 25, 2005 #1
    What is the proof that the inner product of two functions f(x) and g(x) is

    [tex]
    \int_{a}^{b} f(x)g(x)dx
    [/tex]

    Or is this actually a definition of the inner product for functions? If it is a definition, then what is it based on?

    Thank you
     
    Last edited: Apr 25, 2005
  2. jcsd
  3. Apr 25, 2005 #2

    arildno

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    You've gotten it backwards:
    That particular integral can be shown to fulfill the PROPERTIES OF AN INNER PRODUCT.

    For your info, if w(x) is a positive integrable function, the following can also be shown to be an inner product:
    [tex]<f,g>\mid_{w}=\int_{a}^{b}f(x)g(x)w(x)dx[/tex]
     
  4. Apr 25, 2005 #3
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