In your expression for the and (wherever they appear), on the RHS should be and shouldn't they ?
(You got lucky with because
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!
Hi BobP, and thanks for the help.
I don't see why does it matter if I take , or , .
both , and , spans the same vector space, so if a vector is orthogonal to , , it will be orthogonal to , as well.
nevertheless, I tried to take instead, and this is what I get:
which is still not orthogonal to / / /
The formula that you have for comes from the assumption that
To calculate the coefficient (for example) you take the inner product of this equation with
That gets you
from which
That doesn't happen if you use rather than since are not orthogonal.
For the last bit, check your integration.
I get