1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Inner product as integral, orthonormal basis

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Define an inner product on P2 by <f,g> = integral from 0 to 1 of f(x)g(x)dx. find an orthonormal basis of P2 with respect to this inner product.

    2. Relevant equations

    So this is a practice problem and it gives me the answer I just don't understand where it came from. It says, "We first find a basis of P2 then use Gram-Schmidt to create an orthonormal basis. Fix a basis B = {f1(x) = 1, f2(x) = x - 1/2, f3(x) = (x-1/2)2}." then it goes on to use Gram-Schmidt which I understand. I just don't get where the basis came from, if anyone can explain. Thanks!
  2. jcsd
  3. May 5, 2010 #2


    Staff: Mentor

    The standard basis for P2 would be {1, x, x2}, but there are many possible bases, and they just came up with a different one. As long as there are three functions that are linearly independent, the set is a basis, so where it came from shouldn't be a concern. Just take it as a given, and proceed with Gram-Schmidt to find an orthogonal basis, and then normalize each function.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook