Diagonalization goes to 11 when we take on symmetric matrices. The eigenvectors are now always guaranteed to be linearly independent and, almost unbelievably, they form an orthogonal basis for $R^n$. Real symmetric matrices also have real eigenvalues (no rotations). We now write $\mathbf{A} = \mathbf{Q}\mathbf{\Lambda}\mathbf{Q}^{\rm T}$. Even more amazingly, diagonalization now works so that we see $\mathbf{A}$ as a sum of weighted, outer-product-based projection operators. We present the basic story and examine our simple example.