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Orthogonality of Functions

  1. Oct 15, 2004 #1
    We were doing examples in class today and showed that sin and cos were orthogonal functions. In general, is true that even and odd functions are orthogonal? I was unsure where a proof of this might begin, mostly how to generalize the notion of an even or odd function.
     
  2. jcsd
  3. Oct 15, 2004 #2

    matt grime

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    This depends on what your "inner product" is.

    Let's assume it is

    [tex] <f,g> = \int_{-a}^a f(x)g(x)dx[/tex]

    an odd function is one that satisfies f(x) = -f(-x) an even one satisfies f(x)=f(-x)

    1. show that the product of an even and an odd function is odd
    2. show that the integral of an odd function over any interval [-a,a] is zero.
     
  4. Oct 15, 2004 #3
    Thanks. Now that I see it like that I can't believe I couldn't come up with that.
     
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