# Thread: Inner product of polynomial

1. ## Inner product of polynomial

Hey everyone,

My teacher gave a problem to show that p = 1 + x and q = 1 - x are orthogonal, but he says let <p,q> = a0b0 + a1b1 be the inner product. How do I do this with out integrating? I'm a little confused.

Thanks

2. What are $a_{0}, b_{0}, a_{1}, b_{1}?$ I would assume you have something like $p(x)=a_{0}+a_{1}x,$ and $q(x)=b_{0}+b_{1}x.$ If that's so, then the inner product $\langle p,q\rangle=a_{0}b_{0}+a_{1}b_{1}$ will definitely give you orthogonality of those two polynomials. Do you see how?

3. You don't have to integrate because the inner product is not defined by an integral. You only have to apply the definition and see what $a_0$, $a_1$, $b_0$ and $b_1$ are.

4. I see it. It was like you said it was. It would be (1)(1) + ((1)(-1) = 0.

5. That's right.

6. Thanks

7. You're welcome!