Finding Orthogonal Complement

Hi! So I'm not totally sure what to do here...

so if p(x)=x and W = span{p} what is W^{⊥} ?

I thought I would use {1,x} as a basis and then

u_{1} = 1

u_{2} = 1 - proj_{u1}(v_{2})

so then u_{2} = 1 - (<1,x>/<1,1>)*1

That didn't really seem to come out right though. can anyone help me?

Re: Finding Orthogonal Complement

May i ask in what inner product space are you in. is it $\displaystyle <f(x), g(x)> = \int_0^1 f(x)g(x) dx $ ?

Also, what vector space are you working in?

Re: Finding Orthogonal Complement

Quote:

Originally Posted by

**jakncoke** May i ask in what inner product space are you in. is it $\displaystyle <f(x), g(x)> = \int_0^1 f(x)g(x) dx $ ?

Also, what vector space are you working in?

Yes, only the limits on the integral are -1 to 1.

An earlier part of the question says it's in P2