# Gram - Schmidt Orthogonalization

• May 13th 2010, 03:45 AM
Silver
Gram - Schmidt Orthogonalization
I have been trying to do this question and I keep getting $\displaystyle v_3$ different to what my lecturer has in the notes. Can anyone please find $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$ for me?!

The question is:

Quote:

Apply the Gram-Schmidt orthogonalization procedure to the R-basis $\displaystyle \{{1, x, x^2, x^3}\}$ to obtain an orthonormal basis for $\displaystyle P_3(R)$ where the inner product is defined by

$\displaystyle \int_{-1}^{1} (1-x^2)f(x)g(x) \, dx$

The equations used in the process are here

I dont need the working out, I just want to know the final answers for $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$. Thank you!
• May 13th 2010, 04:14 AM
tonio
Quote:

Originally Posted by Silver
I have been trying to do this question and I keep getting $\displaystyle v_3$ different to what my lecturer has in the notes. Can anyone please find $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$ for me?!

The question is:

The equations used in the process are here

I dont need the working out, I just want to know the final answers for $\displaystyle v_1$, $\displaystyle v_2$ and $\displaystyle v_3$. Thank you!

Instead of doing all the lengthy GM process tell us what's what you get and what's what your lecturer gets: this stuff is fairly simple to check, because the result must be orthonormal...(Wink)
That way we can decide who's wrong ,where and why.

Tonio
• May 13th 2010, 04:16 AM
Silver
I actually got it now, sorry about that :P
I didnt cancel something at some point and it gave me totally different answer! I just had to be more careful! Thank you anyways!