# Math Help - Finding an Orthonormal Basis

1. ## Finding an Orthonormal Basis

The inner product here is defined by the integration of p(x)q(x) from 0 to 1.

I sort of understand why this is true, but I can't prove it (so I guess I don't fully understand it).

2. Originally Posted by davismj

The inner product here is defined by the integration of p(x)q(x) from 0 to 1.

I sort of understand why this is true, but I can't prove it (so I guess I don't fully understand it).

Why did you choose precisely that basis for $P_2[x]_{\mathbb{R}}$? Check that wrt the basis $\{1,x,x^2\}$, the matrix of the diff. operator ALREADY is upper triangular, so just carry on the GS process on this basis...