# Thread: Find the projection of the function

1. ## Find the projection of the function

Let V = C([-1,1]), with the inner product <f,g> = ∫-1,1 f(t)g(t) dt,

and let W be the subspace R<=2[x] ⊂ V, with basis the Legendre polynomials {1, x, 3x2-1}.

Find the projection of the function f(t) = et onto W using this basis.

I am completely lost there is too much going on in this problem.. and my professor never really explained projections with integrals, or legendre polynomials, etc. Any help?

2. ## Re: Find the projection of the function

Hey TimsBobby2.

Remember that your final vector will be v(t) = a_t*a + b_t*b + c_t*c and if (a,b,c) are orthogonal to each other then a_t is the inner product of the function against the vector a that is normalized, with the same for b and c respectively.

First figure out the normalized vectors (if they aren't already normalized) and take the inner product of your function with respect to those vectors.

3. ## Re: Find the projection of the function

Would I use the legendre polynomials to figure out the normalized vectors? That's where I'm having the trouble I suppose. I'm not sure what to use to begin.

4. ## Re: Find the projection of the function

If they are orthogonal, then they will be the vectors. Normalizing them is just dividing by SQRT(<v,v>) like you do with normal vectors. If this term is 1, then they are normalized.