find an orthonormal basis of polynomials of degree 2 over the real space, with inner product <p,q> = integral from (0,1) of p(x)q(x)dx.

if you could direct me as to how to insert an integral symbol that would be great as well!

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- April 22nd 2008, 04:31 PMmathisthebestpuzzlefinding an orthonormal basis
find an orthonormal basis of polynomials of degree 2 over the real space, with inner product <p,q> = integral from (0,1) of p(x)q(x)dx.

if you could direct me as to how to insert an integral symbol that would be great as well! - April 22nd 2008, 09:53 PMCaptainBlack
You start with a known basis say then apply the Gramm-Schmidt process to generate an orthogonal basis, and then normalise the new basis.

RonL

(To typeset mathematics this site uses LaTeX, see the tutorial here) - April 22nd 2008, 10:11 PMmathisthebestpuzzle
can you explain the normalization of the orthonormal basis? i have found the gramm-schmidt applied to the 1, x, and x^2. what must i do to normalize?

ps. you're a baller. - April 22nd 2008, 10:19 PMIsomorphism
- April 22nd 2008, 10:23 PMCaptainBlack