Inner product

  • Thread starter keddelove
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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:

matt grime

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You set f(x)=x^p and g(x)=x^q.
 

HallsofIvy

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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]
 

AKG

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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]
And you can give an exact number equal to that last expression.
 

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