Thread: 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
u₁ = 1
u₂ = 1 - proj_u1(v₂)

so then u₂ = 1 - (<1,x>/<1,1>)*1

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

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?

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