Find the orthogonal complement to the linear subspace of polynomials

[resepti]

Find the orthogonal complement to the linear subspace of polynomials to the powers of no higher than n, whose coefficients at even powers are zero. Find its basis and dimension Please help

 

[stapel]

Find the orthogonal complement to the linear subspace of polynomials to the powers of no higher than n, whose coefficients at even powers are zero. Find its basis and dimension Please help

What are your thoughts? What have you tried? How far have you gotten?

Please be complete, even if you think your work is wrong, so the helpers can see what's going on. Thank you!

Eliz.