Is integration of polynomial a bilinear for

[jut24]

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

 

[Hurkyl]

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.

 

[HallsofIvy]

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 $\int_0^1 f(x)(ag(x)+ bh(x))dx= a\int_0^1 f(x)g(x)dx+ b\int_0^1 f(x)h(x)dx$?

 

[x0104]

on this topic:

this bilinear form is non-degenerate right?

I'm not exactly sure how to show that though...

 

[HallsofIvy]

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