I was reading the wikipedia page for symmetric matrices, and I noticed this part:
a real n×n matrix A is symmetric if and only if there is an orthonormal basis of Rn consisting of eigenvectors for A
Does this mean the eigenvectors of a symmetric matrix with real values always form an orthonormal basis, meaning that without changing them at all, they're always orthogonal and always have a norm of 1?
Or does it mean that based on the eigenvectors, we can manipulate them (e.g. divide them by their current norm) and turn them into vectors with a norm of 1?