1. ## gram-schmidt procedure

I could use some help with the following...

On $P_{2}(R)$, consider the inner product given by $=\int_0^1 p(x)q(x) dx$. Apply the Gram-Schmidt procedure to the basis $(1,x,x^2)$ to produce an orthonormal basis of $P_{2}(R)$.

2. Originally Posted by zebra2147
I could use some help with the following...

On $P_{2}(R)$, consider the inner product given by $=\int_0^1 p(x)q(x) dx$. Apply the Gram-Schmidt procedure to the basis $(1,x,x^2)$ to produce an orthonormal basis of $P_{2}(R)$.
Okay, well, what do you understand as the"Gram-Schmidt procedure"? To start with you will want unit vectors. What is the length of the vector "1"? What is the inner product of "1" and "x"?

3. Well, the way I understand it is that we are trying to find an orthonormal list of vectors in V. Here is the procedure that I believe is accurate...
$e_1=v_1/||v_1||$
$e_2=v_{2}-e_{1}$ where $e_1$ is the projection of $v_2$ onto $e_1$. This process continues for all $e_j$.
The length of vector 1 is 1.
And the inner product of 1 and x is just x I believe.