02 - Spectral Theorem

Spectral Theorem

Let $A:\mathcal{H}\to \mathcal{H}$ be a map where $\mathcal{H}$ is a finite-dimensional complex inner product space

If $A$ is self-adjoint then
There exists an orthonormal basis of eigenvectors for $A$

Note that for eigenvalues with two or more linearly independent eigenstates then use Gram-Schmidt