I know how to do a Gram-Schmidt procedure. What I don't understand is how to show that the matrix for the differentiation operator on the orthonormal basis (1,sqrt(3)(2x-1),sqrt(5)(6x^2-6x+1)) is upper triangular...
I know how to do a Gram-Schmidt procedure. What I don't understand is how to show that the matrix for the differentiation operator on the orthonormal basis (1,sqrt(3)(2x-1),sqrt(5)(6x^2-6x+1)) is upper triangular...
Why did you choose precisely that basis for $\displaystyle P_2[x]_{\mathbb{R}}$? Check that wrt the basis $\displaystyle \{1,x,x^2\}$, the matrix of the diff. operator ALREADY is upper triangular, so just carry on the GS process on this basis...