## Spectral Theorem

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# Spectral theorem

Theorem 3.1   (Spectral Theorem) . Suppose $\hat{A}$ is a compact self-adjoint operator on a Hilbert space $\mathcal{H}$ then, there is an orthonormal basis of $\mathcal{H}$ consisting of eigenvectors of $\hat{A}$. Each eigenvalue of $\hat{A}$ is real.

Cecilia Flori 2007-01-02