Is <p,q> = p(0)q(0) + p(1)q(1) an inner product on P2?

[Mona1990]

Hi,
I was wondering how would i determine if <p,q> = p(0)q(0)+ p(1)q(1) is an inner product for P2.

I know, we have to check for non-negativity, symmetry and linearity. Just not sure how.

thanks!

 

[lanedance]

what is P2?

try working through the definitions using what you know about P2

for the first can you show
<p,q> = p(0)q(0)+ p(1)q(1) >= 0
or can you find a counter example or reason why this is not the case?