§ Spectral norm of Hermitian matrix equals largest eigenvalue (TODO)

Define Amax{Ax:x=1}||A|| \equiv \max \{ ||Ax|| : ||x|| = 1 \}. Let AA be hermitian. We wish to show that A||A|| is equal to the largest eigenvalue. The proof idea is to consider the eigenvectors v[i]v[i] with eigenvalue λ[i]\lambda[i] with largest eigenvalue vv^\star of eigenvalue λ\lambda^* and claim that Av=λ||Av^\star|| = \lambda^* is maximal.