Is integration of polynomial a bilinear for

1. Oct 27, 2008

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

2. Oct 27, 2008

Hurkyl

Staff Emeritus
Directly.

3. Oct 27, 2008

HallsofIvy

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

4. Nov 6, 2008

x0104

on this topic:

this bilinear form is non-degenerate right?

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

5. Nov 7, 2008

HallsofIvy

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