But of course
Challenging (more or less) question. I put it in this subforum as to avoid giving hints on the way to solve it.
My friend told me a method, but I'm curious to know if there are others.
So we have a polynomial such that its degree ,
prove that .
Remember that (the 0 polynomial ) by the definition of inner-product
Okay, let be the space of polynomials of degree less or equal than over R. (our field will be R)
We define: by:
You can check that this is an inner-product.
Now is a basis of
And is orthogonal to each of them, hence it's orthogonal to all vectors of just see that . (in particular to itself and hence )