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Function inner product

  1. Aug 11, 2007 #1
    Dear all:
    I have a problem about the inner product of a function. Give a function

    [tex]
    \begin{displaymath}
    f(x) = \left\{ \begin{array}{ll}
    x & \textrm{if $x \in [0,1]$}\\
    -x+2 & \textrm{if $x \in (1, 2]$}
    \end{array}
    \end{displaymath}
    \{[/tex]

    What's the value of the inner product of the function itself over [0,2]?
    [tex]
    \begin{displaymath}
    <f(x), f(x)> = \int_{x=0}^{x=2} f(x)f(x) d_x
    \end{displaymath}
    [/tex]]

    If given another function
    [tex]

    g(x) = \left\{ \begin{array}{ll}
    x-1 & \textrm{if $x \in [1,2]$}\\
    -x+3 & \textrm{if $x \in (2, 3]$}
    \end{array}

    \{[/tex]

    What's the inner product of f(x) and g(x) please?

    Thanks for answering.
     
    Last edited: Aug 11, 2007
  2. jcsd
  3. Aug 11, 2007 #2
    For you first question you have to seperate integral into two
    One of them is from 0 to 1, the other is from 1 to 2.

    For the second you have to explain on which interval we take the inner product they are from different worlds.
     
  4. Aug 11, 2007 #3
    I know the principle actually. Could you give me the whole details please? Because I can't get the correct answer.
     
  5. Aug 11, 2007 #4
    For question1
    You have to get from integral(0-1) =1/2 and from integral(1-2) =1/3
    If you did not then write what you did .Maybe we can find the mistake
    It would be yours or mine
     
    Last edited: Aug 11, 2007
  6. Aug 11, 2007 #5
    for question 2 : I am still waiting an explanation
    It can be only defined on [1,2] i think
     
    Last edited: Aug 11, 2007
  7. Aug 11, 2007 #6
    It's possible that the intention is that f and g vanish wherever not explicitly defined. Then you would be right, it would be like on [1,2]...
     
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