I have been told that orthonormalization of the eigenvectors of a non-hermitian matrix has to use a different definition of inner product than when the matrix is hermitian. Why is this so, and how do I orthonormalize non-hermitian matrix eigenvectors?
I think it has to do with the fact that there are complex exponentials in my matrix, and that by taking their complex conjugate, I don't satisfy hermitian-ness.