Orthonormality of basis:

1
Function Space
Orthonormality of basis
A dot product in a real vector space is a row
vector times a column vector. The way we
transpose in a complex function space is to
apply complex conjugate.
2
Dirac delta is the limit of a sequence of
ever-narrower, ever higher functions with Area1
3
Function Space
How we did this in vector space
Projection onto basis
The Dirac delta picks out the value of A(k)
when kk
4
Also
5
Gaussian
Is a special function for Fourier transforms.
Pythagorean theorem