I want to have linearly independent combinations of f and g that are orthognal on the interval from (-1,1) I'm guesing that they need to be wrt f and g.
If I have two eigenfunctions of an operator with the same eigenvalue how do I construct linear combinations of my eigenfunctions so that they are orhtogonal?
My eigenfunctions are: f=e^(x) and g=e^(-x)
and the operator is (d)^2/(dx)^2