Transforming inner product to another basis

[Kruger]

Homework Statement

Given the Vectorspace V of the real polynoms and the sub space L(1, t, t^2). On V there's a inner product defined as follows:

<u(t), w(t)> = integral(u(t)*w(t), dt, -3, 3)

I have to find the inner product of the subspace in reference of the basis (1, t, t^2).

Homework Equations

The only thing I know is that every innerproduct can be represented by a symmetric matrix.

The Attempt at a Solution

Give me some hints, ... thanks

 

[NateTG]

The the inner product you have listed is independent of the basis. Perhaps you're expected to write out both versions as matrices?

p.s. If you know how, Latex makes things easier to read:
$$<v(t),u(t)>=\int_{-3}^{3}v(t)*u(t) dt$$

 

[Kruger]

Sorry, I cannot use this Latex editor.

But you're right, I have to write out the inner product (in reference ot the basis I wrote down) in the matrix version.

 

[MathematicalPhysicist]

well write iT as:
<a0+a1t+a2t^2,b0+b1t+b2t^2>=A^tGB
where A=(a0,a1,2)^t B=(b0,b1,b2)^t
now you say you know how G is, then you know how to calculate it.
btw, G is a 3x3 symmetric matrix.

 

[Kruger]

Ok, this seems sensible. I try to calculate G. ...