Is it sufficient to diagonalize overlap matrix (Gram matrix) in order to find orthogonalized basis? Overlap matrix $G$ can be diagonalized as $P^{-1} G P=\lambda$. My new set of vectors would be $\tilde{\mathbf{n}_i}=\frac{1}{\sqrt{\lambda_i}} \mathbf{n}_i P$, where $\lambda_i$ is the corresponding eigenvalue. Can sb explain what is the problem with this method?
2026-03-25 09:26:11.1774430771
Orthonormalization of basis - Diagonalization of overlap matrix.
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