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Is integration of polynomial a bilinear for

  1. Oct 27, 2008 #1
    Hello,

    I am begin billinear form and need help with a proof

    say you have an integral from 0 to 1 f(x)g(x) is it bilinear if show how do you prove that it is.
    2) Can someone explain the significance of kroenecker delta.



    Jut24
     
  2. jcsd
  3. Oct 27, 2008 #2

    Hurkyl

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    Directly.
     
  4. Oct 27, 2008 #3

    HallsofIvy

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    In other words, you prove that [itex]\int f(x)g(x)dx[/itex] is bilinear by showing that it satisfies the definition of "bilinear":

    Is [itex]\int_0^1 (af(x)+ bg(x))h(x)dx= a\int_0^1 f(x)h(x)dx+ b\int_0^1 g(x)h(x)dx[/itex]?
    Is [itex]\int_0^1 f(x)(ag(x)+ bh(x))dx= a\int_0^1 f(x)g(x)dx+ b\int_0^1 f(x)h(x)dx[/itex]?
     
  5. Nov 6, 2008 #4
    on this topic:

    this bilinear form is non-degenerate right?

    I'm not exactly sure how to show that though...
     
  6. Nov 7, 2008 #5

    HallsofIvy

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    Well, what is the definition of "non-degenerate"?
     
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