Let V be the complex inner product space consisting of all continuous funtion on [-pi,pi] with the inner product defined as
=the integral from -pi to pi of f times g
Now I know that it is easy to prove that the set of functions {sin(x), cos(x), sin(2x), cos(2x), ,,,} for all n natural is orthogonal because it is easy to show that the inner product
= 0 for all m,n natural numbers
= = 0 if m doesn't equal n
My question is that is this not also true for all m,n where m doesn't equal n. Why does this only work when m,n are restricted to natural numbers?
I have seen and done the proof (while trying to work with Fourier Series) and it seems to me that it should for for ALL m and n instead of just natural number.
2006-10-23
19:00:01
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2 answers
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asked by
The Prince
6
in
Mathematics