Is integration of polynomial a bilinear for

jut24
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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
 
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jut24 said:
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.
Directly.
 
In other words, you prove that \int f(x)g(x)dx is bilinear by showing that it satisfies the definition of "bilinear":

Is \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?
Is \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?
 
on this topic:

this bilinear form is non-degenerate right?

I'm not exactly sure how to show that though...
 
Well, what is the definition of "non-degenerate"?
 
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