Hi guys.

I have the following base for :

I want to orthogonalize this base with respect to the inner product:

somthing doesn't add up, and I suspect that I have made some calculation error, even though I checked several times.

so let's say the new orthogonal base will be

I first set .

then:

(I checked it - it is correct, since it's orthogonal to , which is 1)

but when I try to find , I get:

so this is what I get, but is NOT orthogonal to neither or !

any help would be greatly appreciated!