Gram - Schmidt Orthogonalization

Feb 2008
40
6
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:

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!
 
Oct 2009
4,261
1,836
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
 
Feb 2008
40
6
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!