Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inner product

  1. Jan 5, 2007 #1
    Hello, I am working on an assignment were I have shown that a certain equation defines an inner product, which was simple enough. Te equation was:

    [tex] \left\langle {f,g} \right\rangle = \int\limits_0^1 {f\left( x \right)g\left( x \right)x^2 dx} [/tex]


    My question then is: How do i state an equation for the inner product of x^p and x^q.

    Sorry if the information is sparse
     
    Last edited: Jan 5, 2007
  2. jcsd
  3. Jan 5, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You set f(x)=x^p and g(x)=x^q.
     
  4. Jan 5, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Looks straight forward to me. If
    [tex]<f,g>= \int_0^1 f(x)g(x)x^2 dx[/tex]
    f(x)= xp, and g(x)= xq, then
    [tex]<f,g>= \int_0^1 (x^p)(x^q)x^2dx= \int_0^1 x^{p+q+2}dx[/tex]
     
  5. Jan 5, 2007 #4

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    And you can give an exact number equal to that last expression.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Inner product
  1. Inner products (Replies: 5)

  2. Inner product (Replies: 2)

  3. Inner product (Replies: 2)

  4. Inner Product (Replies: 10)

  5. Inner Products? (Replies: 7)

Loading...